Experimental and numerical evaluations of stress relaxation in A356 aluminium alloy subjected to out-of-phase thermomechanical cyclic loadings

Abstract

In this study, the stress relaxation has been measured experimentally and has been also calculated numerically by the finite element method in the A356·0 aluminium–silicon–magnesium alloy, under out-of-phase thermomechanical cyclic loadings. To get this objective, strain based thermomechanical fatigue tests were performed on cylindrical specimens, at an out-of-phase condition. In this loading condition, when the temperature was maximum, the mechanical strain was compressive and vice versa. These fatigue experiments were repeated at various dwell times, in which the temperature was held at the maximum temperature. This hold time was considered as 5, 30, 60 and 180 s and then the stress relaxation was measured during the mid-life cycle of each test. Besides, the finite element analysis was also conducted on the material to simulate the stress relaxation numerically. A two-layer visco-plastic model was applied to simulate the high temperature cyclic behavior of the material. Finite element results showed a good agreement with experimental results, which were obtained from thermomechanical fatigue tests on the A356·0 aluminium alloy. The two-layer visco-plastic model could properly predict the stress relaxation at elevated temperatures, during various dwell times.     

Creep crack growth rate predictions in 316H steel using stress dependent creep ductility

Abstract

Short and long term trends in creep crack growth (CCG) rate data over test times of 500–30?000 h are available for Austenitic Type 316H stainless steel at 550°C using compact tension, C(T), specimens. The relationship between CCG rate and its dependence on creep ductility, strain rate and plastic strain levels has been examined. Uniaxial creep data from a number of batches of 316H stainless steel, over the temperature range 550–750°C, have been collected and analysed. Power-law correlations have been determined between the creep ductility, creep rupture times and average creep strain rate data with stress σ normalised by flow stress σ_0·2 over the range 0·2<σ/σ_0·2<3 for uniaxial creep tests times between 100 and 100?000 h. Creep ductility exhibits upper shelf and lower shelf values which are joined by a stress dependent transition region. The creep strain rate and creep rupture exponents have been correlated with stress using a two-stage power-law fit over the stress range 0·2<σ/σ_0·2<3 for temperatures between 550 and 750°C, where it is known that power-law creep dominates. For temperature and stress ranges where no data are currently available, the data trend lines have been extrapolated to provide predictions over the full stress range. A stress dependent creep ductility and strain rate model has been implemented in a ductility exhaustion constraint based damage model using finite element (FE) analysis to predict CCG rates in 316H stainless steel at 550°C. The predicted CCG results are compared to analytical constant creep ductility CCG models (termed NSW models), assuming both plane stress and plane strain conditions, and validated against long and short term CCG test data at 550°C. Good agreement has been found between the FE predicted CCG trends and the available experimental data over a wide stress range although it has been shown that upper-bound NSW plane strain predictions for long term tests are overly conservative.     

Artificial neural network modelling to predict hot deformation behaviour of as HIPed FGH4169 superalloy

Abstract

The hot deformation behaviour of as HIPed FGH4169 superalloy was studied by single stroke compression test on MMS-200 test machine at the temperatures of 950–1050°C and the strain rates of 0·004–10 s^?1. Based on the experimental results, a back-propagation artificial neural network model and constitutive equation method were established to predict the flow stress of FGH4169 superalloy. The predictability of two different models was compared. The correlation coefficients of experimental and predicted flow stress with the trained BP ANN model and constitutive equation were 0·9995 and 0·9808 respectively. The average root mean square error (RMSE) values of the trained ANN model and constitutive equation are 0·39 and 2·21 MPa respectively. And the average absolute relative error (AARE) values of the trained ANN model and constitutive equation are 1·79 and 7·47% respectively. The results showed that the ANN model is an effective tool to predict the flow stress in comparison with constitutive equation.     

Creep cavity nucleation and growth in 12Cr–Mo–V steel

Abstract

Quantitative measurements of the number of cavities per unit area, mean cavity size, and cavitated area fraction are carried out on creep tested specimens of a 12Cr–Mo–V martensitic steel. Both interrupted and ruptured specimens are included. Cavities initiate at an early stage of tests. The number of cavities, mean cavity size, and cavitated area fraction exhibit a continued increase with increasing strain and time. At rupture, the number of cavities is about 30 000 mm^?2, and the mean cavity size has a maximum value of about 2·5 μm.The cavitated area fraction is approximately 0·1% at 1% strain, 0·5% at 2% strain, and 10% at rupture. Cavity initiation and growth are analysed regarding temperature, stress, strain, and strain rate. A constrained cavity growth model is discussed and compared with the experimental results.

MST/3097     

Effect of heat treatment on fatigue crack growth in chain steels

Abstract

The influence of tempering temperature, stress ratio, and prior strain on fatigue crack propagation in a low-alloy chain steel has been investigated. At small stress ratios (R=0·1) tempering above 400°C is beneficial, resulting in higher threshold levels and slower growth rates in the initial growth regime. Thereafter, crack growth is independent of tempering temperature, as it is over the entire growth period under a high mean stress (R=0·5). Prior strain produces a slower growth and higher thresholds at R= 0·1. Intergranular fracture is common and is a function of stress intensity range and tempering temperature. It is concluded that residual stress effects, rather than microstructural effects, account for the experimental observations. In particular, the existence of a tensile residual stress during initial growth and a crack closure stress greater than the minimum applied stress level are proposed.

MST/672     

Experimental and numerical analyses of mean stress relaxation in cold expanded plate of Al‐alloy 2024‐T3 in double shear lap joints

In this paper, the mean stress relaxation behavior of simple Al‐alloy 2024‐T3 specimens and also the mean stress relaxation around the hole of cold expanded specimen are studied. The analyses are performed through the combination of the nonlinear isotropic hardening and Chaboche nonlinear kinematic hardening model accompanied by the results of experimental tests. The strain‐controlled axial tests are performed at two different strain amplitudes, while the stress‐controlled tests of cold expanded specimens are performed for three different imposed load amplitudes. The constitutive equations of the hardening model are coded as a UMAT subroutine in FORTRAN programming language and implemented in the commercial finite element code of ABAQUS. The accuracy of the hardening model has been proved in two steps: first by simulations of mean stress relaxation during the uniaxial strain‐controlled cyclic tests and second by simulation of strain ratcheting during the stress‐controlled cyclic loading. The stress and strain distributions after cold expansion process are examined as well as the mean stress relaxation due to cyclic loading. The results show the influences of imposed stress amplitude on increasing mean stress relaxation and also the effect of cold expansion level on reducing the mean stress relaxation.     

Effect of epitaxial ferrite on yielding and plastic flow in dual phase steel in tension and compression

Abstract

A low carbon, microalloyed steel was heat treated to obtain dual phase microstructures containing constant levels of 18 and 25 vol.-% martensite at two levels of microstructural refinement and with varying epitaxial ferrite content. Tensile and compression tests were conducted at a strain sensitivity of 2 × 10^-5. Elastic limits in tension and compression were indistinguishable and very low, suggesting that mobile dislocations were present in the ferrite as a consequence of stress relaxation processes. These mobile dislocations accommodated the volume increase accompanying the austenite to martensite transformation during heat treatment. Epitaxial ferrite had little effect on the 0·2% proof stress, but average proof stresses were generally higher in compression than in tension owing to residual stresses in the martensite and ferrite following heat treatment. The residual stresses calculated from this asymmetry in the proof stresses were small because of stress relaxation in the ferrite at the temperature at which the martensite formed. Epitaxial ferrite significantly increased uniform elongation in tension with a small decrease in tensile strength for both levels of martensite in the finer microstructure but only at the 18 vol.-% martensite level in the coarser microstructure. The cause of the increased ductility was the effect of epitaxial ferrite on the work hardening rate between approximately 0·5 and 3% strain; epitaxial ferrite reduced the work hardening rate in this range of strain.     

Hot deformation behaviour of precipitation hardening stainless steel

Abstract

The behaviour of 17-4 precipitation hardening (PH) stainless steel was studied using the hot compression test at temperatures of 950–1150°C with strain rates of 0·001–10 s^?1. The stress–strain curves were plotted by considering the effect of friction. The work hardening rate versus stress curves were used to reveal whether or not dynamic recrystallisation (DRX) occurred. Using the constitutive equations, the activation energy of hot working for 17-4 PH stainless steel was determined as 337 kJ mol^?1. The effect of Zener–Hollomon parameter Z on the peak stress and strain was studied using the power law relation. The normalised critical stress and strain for initiation of DRX were found to be 0·89 and 0·47 respectively. Moreover, these behaviours were compared to other steels.     

Effect of process parameters on deformation and temperature rise during forging of TC6 alloy disc

Abstract

Effect of the deformation temperature, hammer velocity, height reduction and shear factor on the equivalent stress, strain and temperature rise has been studied in forging process of a TC6 titanium alloy disc with deformation temperatures of 1153–1213 K, hammer velocities of 1·2–12 000 mm min^?1 and shear factors of 0·1–0·4. The calculated results show that the deformation temperature, hammer velocity and height reduction have a significant effect on the equivalent stress and temperature rise, but have a slight effect on the equivalent strain. The predicted load–displacement curves are found to be in a good agreement with the experimental results.     

Effects of prestrain and strain rate on dynamic deformation characteristics of 304L stainless steel: Part 1—Mechanical behaviour

Abstract

A split Hopkinson bar is used to investigate the effects of prestrain and strain rate on the dynamic mechanical behaviour of 304L stainless steel, and these results are correlated with microstructure and fracture characteristics. Annealed 304L stainless steel is prestrained to strains of 0·15, 0·3, and 0·5, then machined as cylindrical compression specimens. Dynamic mechanical tests are performed at strain rates ranging from 10² to 5 × 10³ s^-1 at room temperature, with true stains varying from 0·1 to 0·3. It was found that 304L stainless steel is sensitive to applied prestrain and strain rate, with flow stress increasing with increasing prestrain and strain rate. Work hardening rate, strain rate sensitivity, and activation volume depend strongly on the variation of prestrain, strain, and strain rate. At larger prestrain and higher strain rate, work hardening rate decreases rapidly owing to greater heat deformation enhancement of plastic flow instability at dynamic loading. Strain rate sensitivity increases with increasing prestrain and work hardening stress (σ-σ_y). However, activation volume exhibits the reverse tendency. Catastrophic fracture is found only for 0·5 prestrain, 0·3 strain, and strain rate of 4·8 × 10³ s^-1. Large prestrain increases the resistance to plastic flow but decreases fracture elongation. Optical microscopy and SEM fracture feature observations reveal adiabatic shear band formation is the dominant fracture mechanism. Adiabatic shear band void and crack formation is along the direction of maximum shear stress and induces specimen fracture.     

Prediction of dynamic recrystallisation behaviour of AISI type 4140 medium carbon steel

Abstract

The aim of the present work was to establish quantitative relationships between the flow stress and the volume fraction of dynamic recrystallisation (DRX) as a function of processing variables such as strain rate, temperature, and strain for AISI type 4140 medium carbon steel, by means of torsion tests. Torsion tests were carried out in the temperature range 900-1100°C and the strain rate range 5·0 × 10­2 -5·0 × 10⁰ s^­1 to study the high temperature softening behaviour. For the exact prediction of flow stress, the effective stress—effective strain curves were divided into two regions, the work hardening and dynamic recovery region and the DRX region. The flow stress of the DRX region could be expressed in terms of the volume fraction of DRX. It was found that the calculated results were in agreement with the experimental flow stress and microstructure of the steel for any deformation condition.     

Investigation on hot deformation of 20Cr–25Ni superaustenitic stainless steel with starting columnar dendritic microstructure based on kinetic analysis and processing map

Abstract

The deformation behaviour of a 20Cr–25Ni superaustenitic stainless steel (SASS) with initial microstructure of columnar dendrites was investigated using the hot compression method at temperatures of 1000–1200°C and strain rates of 0·01–10 s^?1. It was found that the flow stress was strongly dependent on the applied temperature and strain rate. The constitutive equation relating to the flow stress, temperature and stain rate was proposed for hot deformation of this material, and the apparent activation energy of deformation was calculated to be 516·7 kJ mol^?1. Based on the dynamic materials model and the Murty’s instability criterion, the variations of dissipation efficiency and instability factor with processing parameters were studied. The processing map, combined with the instability map and the dissipation map, was constructed to demonstrate the relationship between hot workability and microstructural evolution. The stability region for hot processing was inferred accurately from the map. The optimum hot working domains were identified in the respective ranges of the temperature and the strain rate of 1025–1120°C and 0·01–0·03 s^?1 or 1140–1200°C and 0·08–1 s^?1, where the material produced many more equiaxed recrystallised grains. Moreover, instability regimes that should be avoided in the actual working were also identified by the processing map. The corresponding instability was associated with localised flow, adiabatic shear band, microcracking and free surface cracks.     

Analysis of constitutive behaviours and processing map of 7020 aluminium alloy

Abstract

The authors present a study on the hot formability of 7020 aluminium alloy. Isothermal hot compression tests of solid cylindrical specimens were performed in the temperature range of 300–550°C and the strain rate range of 0·001–10 s^–1. Stress–strain curves obtained from the experiment data are fitted using the Sellars–Tegart constitutive equation to obtain the constitutive parameters. Using the dynamic material model, the authors develop a processing map based on the flow stress data. The map shows that the parameters suitable for hot working are a temperature range of 450–550°C and a strain rate range of 0·001–0·1 s^–1. This parameter range is where the efficiency of power dissipation is above 27% and where dynamic recrystallisation occurs. Unstable regions to be avoided in hot forming are deduced from an instability condition. The processing map is validated by comparing the microstructures of deformed compression specimens.     

Compressive behaviour capable of predicting hot tensile ductility behaviour in a 0·1%C–Mn steel

Abstract

Compression testing was carried out on 0·1%C–0·9%Mn steel at various temperatures and strain rates. Peak strain behaviour was investigated as function of temperature and strain rate. Normalisation of flow stress in the stress–strain curves by peak stress exhibits an interesting trend that the normalised value changes as strain, strain rate and temperature vary. Three regions could be characterised based on the way that the softening factor defined as the difference in normalised value between the peak stress and the flow stress at a strain of 0·5 changes with temperature. It was shown that tensile elongation behaviour could be predicted based on the softening factor determined in compression tests. As the softening factor increases, tensile ductility increases.     

Plastic flow and microstructural evolution in Ti–6Al–2Zr–1Mo–1V alloys during hot deformation

Abstract

The hot deformation behaviour and microstructural evolution in Ti–6Al–2Zr–1Mo–1V alloys have been studied using isothermal hot compression tests. The processing map was developed at a true strain of 0·7 in the temperature range 750–950°C and strain rate range 0·001–10 s^?1. The corresponding microstructures were characterised by means of a metallurgical microscope. Globularisation of lamellae occurring to a greater extent in the range 780–880°C and 0·001–0·01 s^?1 had a peak power dissipation efficiency of 58% at about 850°C and 0·001 s^?1. The specimens deformed in 750–880°C and 0·01–10 s^?1 showed an instability region of processing map, whereas the specimens deformed in 880–950°C and 1–10 s^?1 indicated three kinds of flow instabilities, i.e. macro shear cracks, prior beta boundary cracks and flow localisation bands.     

Effect of superimposed oscillations on creep behaviour of Al – 2 4·.5Cu and Al – 2 4·5Cu – 2 0·1In (wt-%) alloys containing θ′ precipitates

Abstract

The behaviour of both transient and steady state creep of Al – 4·5Cu and Al – 4·5Cu – 0·1In (wt-%) alloys was investigated using a constant stress where torsional oscillations of different frequencies and shear strain amplitudes were operated at various working temperatures. An augment in both transient and steady state creep rates was observed by increasing both frequency and shear strain amplitude of the applied oscillations. The mean values of the activation energy of both alloys for both creep stages were found to be equal to that quoted for dislocation intersection mechanism.     

Effect of notch root radius on tensile behaviour of 316L(N) stainless steel

Abstract

Type 316L(N) stainless steel (SS) is used as the major structural material for high temperature components of sodium cooled fast reactors. The influence of notch root radius on the tensile behaviour of 316L(N) SS under multi-axial stress state was investigated. Double U-notches with five different kinds of notch geometry were incorporated symmetrically into the tensile testing specimens by changing the notch root radius while keeping the gross diameter, net diameter and notch depth as the same for all the notches. The notch root radius was varied as 0·25, 0·5, 1·25, 2·5 and 5 mm. Tensile tests were carried out on the notched specimens at room temperature (298 K) and at 923 K at a constant strain rate of 3×10^?3 s^?1. The tensile strength and yield strength of notched specimen of 316L(N) SS increased with decrease in notch radius at both the temperatures and the notch severity was less pronounced at high temperature. The fractured notch surface was analysed using scanning electron microscope and unfractured notch was sliced along the axis and observed under optical microscope. Finite element analysis was performed on the models of notched specimens with various notch root radii. These results showed that Von Mises equivalent stress which was derived from triaxial stresses decreased with decrease in notch radius. The shift of location of peak values of maximum principal stress and hydrostatic stress towards the axis of the specimen, leading to formation of cracks, occurred at a lower nominal stress when the notch radius was increased.     

Recrystallisation rates in austenite measured by double compression and stress relaxation methods

Abstract

The feasibility of two mechanical testing methods, double compression and stress relaxation, for measuring the static recrystallisation rate in hot deformed austenite was studied. The results were verified by metallographic observations. The effect of recovery on the softening data in an interrupted compression test is eliminated when the reloading flow stresses are analysed at a total strain of 5% instead of the 0.2% offset strain used conventionally. A stress relaxation test provides consistent data on the recrystallisation event. In most instances, the stress present in the course of softening has no effect at all or only slightly enhances the recrystallisation rate. The accelerating effect is most pronounced, about 50-70%, at small strains and fine grain sizes.     

Creep of Pb–2·5Sb–0·2Sn alloy at low stresses

Abstract

The creep of a Pb–2·5Sb–0·2Sn alloy has been studied at stresses up to 6·5 MN m^?2 in the temperature range 318–348 K (0·53–0·58T_m) using helical specimens. At 333 K, a transition in the stress exponent from ~1 to 3 occurred at ~3 MN m^?2. The observed good agreements below the transition stress, both for experimental dE/do and predictions for Coble diffusional creep of lead, and for measured activation energy for creep and the activation energy for grain boundary self-diffusion in lead, suggest that grain boundary diffusional creep is the dominant mechanism. at low stresses. The presence of antimony does not seem to affect the magnitude of dE/do appreciably, and the results suggest that the grain boundary self-diffusivity of lead is not influenced by the presence of segregated antimony on the grain boundaries. The diffusional creep occurred above a threshold stress of magnitude ~0·5 MN m^?2, and its temperature dependence was characterised by an activation energy of ~20 kJ mol^?1, similar to the value of 23 ± 7 kJ mol^?1 typical of pure metals in the temperature range investigated. The stress exponent of ~3 observed for the power law regime suggests control by viscous glide of dislocations constrained by dragging of solute atmospheres. Preliminary tests on sagging beam specimens of as-worked material at an applied stress of 2·5 MN m^?2 and a test temperature of 333 K has provided the first direct evidence that anisotropic grain shape affects Coble creep. The specimen with the longest grain dimension along the stress axis underwent slower creep than the specimen with the longest grain dimension perpendicular to the stress axis. This observation is in qualitative agreement with theoretical predictions.

MST/1139     

Mean stress effects on low‐cycle fatigue for a precipitation‐hardening martensitic stainless steel in different tempers

The objective of this study is to investigate the effects of mean stress and ageing treatment on the low‐cycle fatigue (LCF) behaviour of a precipitation‐hardening martensitic stainless steel (PHMSS). Uniaxial LCF tests were conducted under strain control with three strain ratios, R = ?1, 0 and 0.5 on specimens heat‐treated to three different tempers, i.e. solution‐annealed (SA), peak‐aged (H900) and overaged (H1150) conditions. Experimental results indicated that under a strain ratio of R = ?1, specimens in H900 temper exhibited longer LCF lifetimes than those in SA and H1150 tempers. However, this advantage for H900 over SA and H1150 tempers disappeared at higher strain ratios (R = 0 and 0.5) due to the greater sensitivity to mean stress effects in H900 temper. For a given temper at high strain amplitudes, the LCF lifetimes under the three applied strain ratios did not show significant differences as a result of the mean stress relaxation effect. However, at low strain amplitudes, cyclic loading at R = ?1 generated longer LCF lifetimes in comparison to R = 0 and 0.5 due to the absence of detrimental tensile mean stress. LCF lifetime data obtained for the given PHMSSs under various combinations of strain ratio and heat treatment were well correlated with a strength‐normalized Smith–Watson–Topper (SWT) parameter in a log–log linear model.