Kinetics of scattered fracture in structural metals under elastoplastic deformation

The paper presents a procedure whereby the damage accumulation kinetics in structural materials, such as steel 45, stainless steel 12Kh18N10T, aluminum alloy D16T, and titanium alloy VT22, under elastoplastic deformation is studied based on variation parameters of elastic modulus and resistivity. For complex stress conditions, a continuum model for damage accumulation is proposed which relates the damage parameter to the intensity of accumulated plastic strains. The data calculated by the proposed continuum model are compared to the experimental findings of the investigation of the damage accumulation kinetics for some structural metals. __________ Translated from Problemy Prochnosti, No. 3, pp. 23–34, May–June, 2007.     

Hot deformation behavior of an 8% Cr cold roller steel

An 8% Cr cold roller steel was compressed in the temperature range 900–1200 °C and strain rate range 0.01–10 s⁻¹. The mechanical behavior has been characterized using stress–strain curve analysis, kinetic analysis, processing maps, etc. Metallographic investigation was performed to evaluate the microstructure evolution and the mechanism of flow instability. It was found that the work hardening rate and flow stress decreased with increasing deformation temperature and decreasing strain rate in 8% Cr steel; the efficiency of power dissipation decreased with increasing Z value; flow instability was observed at higher Z-value conditions and manifested as flow localization near the grain boundary. The hot deformation equation and the dependences of critical stress for dynamic recrystallization and dynamic recrystallization grain size on Z value were obtained. The suggested processing window is in the temperature range 1050–1200 °C and strain rate range 0.1–1 s⁻¹ in the hot processing of 8% Cr steel.     

Effect of strain rate on quasistatic tensile flow behaviour of solution annealed 304 austenitic stainless steel at room temperature

Room temperature tensile test results of solution annealed 304 stainless steel at strain rates ranging between 5 × 10⁻⁴ and 1 × 10⁻¹ s⁻¹ reveal that with increase in strain rate yield strength increases and tensile strength decreases, both maintaining power–law relationships with strain rate. The decrease in tensile strength with increasing strain rate is attributed to the lesser amount of deformation-induced martensite formation and greater role of thermal softening over work hardening at higher strain rates. Tensile deformation of the steel is found to occur in three stages. The deformation transition strains are found to depend on strain rate in such a manner that Stage-I deformation (planar slip) is favoured at lower strain rate. A continuously decreasing linear function of strain rate sensitivity with true strain has been observed. Reasonably good estimation for the stress exponent relating dislocation velocity and stress has been made. The linear plot of reciprocal of strain rate sensitivity with true strain suggests that after some critical amount of deformation the increased dislocation density in austenite due to the formation of some critical amount of deformation-induced martensite plays important role in carrying out the imposed strain rate.     

Assessment of damage level in materials by the scatter of elastic characteristics and static strength

The parameters of scatter of elastic characteristics and strength of an aluminum alloy and carbon steel are determined from the results of large-batch tests under identical static deformation conditions. The material degradation is demonstrated to occur in a stagewise manner associated with peculiarities and nature of structural damages accumulated during various deformation stages, which is responsible for nonlinearity of the damage accumulation law. A good correlation has been found between the Weibull homogeneity coefficient and the maximum probability density on lognormal distribution and Weibull distribution curves. Emphasis is put on the advantages of the LM hardness method in terms of information it provides about the integral pattern of material degradation over its lifetime. __________ Translated from Problemy Prochnosti, No. 2, pp. 5–14, March–April, 2006.     

Kinetics of accumulation of scattered damage in polycrystalline materials with various grain sizes under small-scale strain conditions

The paper addresses damage accumulation processes that occur during static deformation in steels 45 and 09G2S and in brass L63 in the initial state and upon “grain annealing.” The authors discuss new experimental evidence on the damage accumulation kinetics during deformation of polycrystalline materials that differ in nature and grain size, including materials in the unloaded state and those under stresses, with small and very small strains (0.05–0.15%). The results obtained have been the necessary physically consistent explanations. Analytical approximations of the correlation between the main mechanical properties of materials (hardness, yield stress, and ultimate strength) and their structure parameters (grain size) are given.     

Analysis of Garofalo equation parameters for an ultrahigh carbon steel

Isothermal stress–strain curves data from torsion tests conducted at high temperature (950–1200 °C) and strain rates (2–26 s⁻¹) were analyzed in an ultrahigh carbon steel (UHCS) containing 1.3%C. The sine hyperbolic Garofalo equation was selected as an adequate constitutive equation for the entire range of the forming variables considered. The Garofalo parameters were assumed strain dependent allowing the prediction of stress–strain curves under transient and steady-state conditions. The average relative errors obtained were below 3% in stress. In addition, the creep deformation mechanisms in the UHCS were analyzed from the Garofalo equation parameters. For this aim, the stress exponent of the Garofalo equation was, for the first time, related to that of the power law equation. The results show that the controlled deformation mechanism at steady state is lattice diffusion-controlled slip creep.     

Constitutive analysis of compressive deformation behavior of ELI-grade Ti–6Al–4V with different microstructures

In this study, a constitutive analysis of the flow responses of Ti–6Al–4V under various strain rates [(e)\dot] \dot{\varepsilon } was conducted by separately quantifying the hardening and softening effects of microstructure, interstitial solute and deformation heating on the total stress. For this purpose, a series of compression tests on an extra-low interstitial grade alloy with equiaxed, lamellar, or bimodal microstructures was performed at 10 ^{- 3} ￡ [(e)\dot] ￡ 10  \texts ^{- 1} 10^{ - 3} \le \dot{\varepsilon } \le 10\;{\text{s}}^{ - 1} until the metal fractured, and the results were compared to those of the commercial grade alloy. The thermal stress σ^* increased with an increasing interstitial solute concentration; the athermal stress increased in the order of equiaxed, lamellar, and bimodal microstructures. Load–unload–reload tests revealed that the flow softening at a relatively high [(e)\dot] \dot{\varepsilon } was likely caused by deformation heating rather than by microstructure change; thus flow softening was attributed to a decrease in σ^*. Finally, a mechanical threshold stress model was extended to capture those observations; the modified model can provide a reasonable prediction of flow stress in Ti–6Al–4V with different microstructures and interstitial solute concentrations.     

Fatigue damage of low amplitude cycles in low carbon steel

The influences of low load cycles on fatigue damage in 0.15% C steel (C15E, No. 1.1141) are investigated in the very high cycle fatigue regime using ultrasonic fatigue testing equipment. Constant amplitude (CA) endurance limits at limiting lifetime of 10⁹ cycles are determined in cyclic tension–compression and cyclic torsion tests. Non-propagating fatigue cracks are found in specimens subjected to cyclic torsion loading at the endurance limit. The endurance limit is considered as maximum stress amplitude where possibly initiated fatigue cracks do not propagate to failure. Two-step variable amplitude (VA) tension–compression endurance tests are performed with repeat sequences consisting of high stress amplitudes above the endurance limit and far greater number of cycles below. The measured lifetimes are compared with linear damage accumulation calculations (Miner calculations). If the high stress amplitude is more than approximately 13% above the CA endurance limit, detrimental influences of low load cycles and failures at low damage sums are found. If the high stress is less than 13% above the CA endurance limit, numerous low load cycles cause prolonged fatigue lifetimes and specimens can sustain large damage sums without failure. Two-step VA fatigue crack growth investigations show that load cycles below the threshold stress intensity accelerate crack growth, if the high stress intensity is 18% or more above the CA threshold stress intensity. In repeat sequences with high stress intensities 14% above threshold stress intensity, low load cycles decelerated and stopped fatigue crack growth. Low load cycles can reduce or prolong fatigue lifetimes of low carbon steel and one reason is the accelerated or retarded fatigue crack growth due to numerous low amplitudes, and the maximum load amplitude of a VA load sequence determines whether detrimental or beneficial effects prevail.     

Coupled modeling of steady-state creep rate and creep rupture strength for metals

New methods of coupled mathematical modeling of steady-state creep rate and creep rupture strength of metals in tension have been devised. Two nonlinear fractional power functions with four material constants are used as basic dependences of the steady-state creep and creep rupture life on stress. Computation of the functions is based on optimally solving two nonlinear and inconsistent — in the conventional meaning — equations sets by the method of minimization of quadratic residuals. The authors outline the methods for calculating material constants, which were used to derive analytical expressions that optimally approximate the test results for 10Kh15N27T3MR steel at 600°C under various stresses. A method of piecewise-linear approximation of creep rupture strength test results, which involves the use of a two-segment broken line, is put forward. It implies that the locations of kinks as well as other numerical characteristics of the broken line are determined from the condition of the line’s optimal arrangement relative to the experimental data points. The method takes a more comprehensive account of various damage accumulation mechanisms in steel under various stress levels. __________ Translated from Problemy Prochnosti, No. 4, pp. 25–35, July–August, 2008.     

Axi-symmetric compression of solid cylinders

Cylinders of EN 24 steel and commercial aluminium were compressed at 0.2 and 10.0 s⁻¹ (rapid loading conditions). The temperature rise due to plastic deformation increased with strain rate and was significantly more in steel than in aluminium. The shape of the observed true stress-true strain curves was similar to the temperature rise-true strain plots. In steel, beyond a certain strain, the flow stress decreased with increasing strain, but in aluminium, a direct relation between the observed true stress and the true strain existed over the entire deformation range. Under rapid loading conditions the ring compression test was more reliable than the Cook and Larke method. In both materials, in specimens of constant diameter up to a true strain of 30%–40%, the compressive yield stress, σ_o, was proportional to H^1/8, where H is the instantaneous height of the specimen. Beyond this strain level, σ_o increased with the diameter-to-height ratio (as seen during slow loading). The various factors that can influence the shape of the observed true stress-true strain curves have been considered. Semi-empirical equations have been developed which ensured that the friction-corrected data covering four to five decades of strain rate superimposed fairly well, following suitable temperature or temperature and strain-rate corrections.     

The kinetics of damage accumulation in heat-resistant steels under different loading conditions

The investigation results are presented for the kinetics of damage accumulation and the process of deformation in a heat-resistant steel 10GN2MFA for different loading conditions under complex stress state.     

Life calculations for materials under irregular nonproportional loading

Experimental data on low-cycle fatigue of 304 steel and a VT9 titanium alloy in deformation by complex loading histories, which are the sequence of blocks of cycles of different shapes in the space of total strains, cited in the literature, are analyzed to develop adequate models for life calculations. The four damage accumulation rules and the low-cycle fatigue deformation criterion were used as basic approaches. Life prediction models were compared. It is shown that the application of a modified nonlinear damage accumulation rule can improve life prediction results, with better outcomes obtained for the programs involving nonproportional cycles. __________ Translated from Problemy Prochnosti, No. 5, pp. 141–150, September–October, 2007.     

Shear stress measurement in nickel and nickel–60 wt% cobalt during one-dimensional shock loading

The shear strength of pure nickel (Ni), and its alloy, Ni–60Co (by wt%), has been determined during one-dimensional shock loading in the impact stress range 0–10 GPa. The influence of the reduced stacking fault energy (SFE) for the Ni–60Co has been investigated. The shear strength (τ) and the lateral stress (σ _y ) both increase with the impact stress for each material. The shear stress has been found to be higher in the nickel than in the alloy. The progressive decrease of the lateral stress behind the shock front indicates an increase of the shear strength. A more complex mechanism of deformation has been found for the alloy since twin formation has been observed in the microstructure, while none has been seen in nickel. It is thought that mechanical twinning plays a predominant role in the deformation mechanism of the alloy resulting in the reduction of the material strength.     

Creep behavior of AZ31 magnesium alloy in low temperature range between 423 K and 473 K

The deformation behavior of coarse-grained AZ31 magnesium alloy was examined in creep at low temperatures below 0.5 T _m and low strain rates below 5 × 10⁻⁴ s⁻¹. The creep test was conducted in the temperature range between 423 and 473 K (0.46–0.51 T _m) under various constant stresses covering the strain rate range 5 × 10⁻⁸ s⁻¹–5 × 10⁻⁴ s⁻¹. All of the creep curves exhibited two types depending on stress level. At low stress (σ/G < 4 × 10³), the creep curve was typical of class I behavior. However, at high stresses (σ/G > 4 × 10³), the creep curve was typical of class II. At the low stress level, deformation could be well described by solute drag creep whereas at the high stress level, deformation could be well described by dislocation climb creep associated with pipe diffusion or lattice diffusion. The transition of deformation mechanism from solute drag creep to dislocation climb creep, on the other hand, could be explained in terms of solute-atmosphere-breakaway concept.     

Processing maps for Fe–24Ni–11Cr–3Ti–1Mo superalloy

Hot deformation characteristics of a Fe-base superalloy were studied at various temperatures from 1000–1200°C under strain rates from 0·001–1 s^− 1 using hot compression tests. Processing maps for hot working are developed on the basis of the variations of efficiency of power dissipation with temperature and strain rate and interpreted by a dynamic materials model. Hot deformation equation was given to characterize the dependence of peak stress on deformation temperature and strain rate. Hot deformation apparent activation energy of the Fe–24Ni–11Cr–1Mo–3Ti superalloy was determined to be about 499 kJ/mol. The processing maps obtained in a strain range of 0·1–0·7 were essentially similar, indicating that strain has no significant influence on it. The processing maps exhibited a clear domain with a maximum of about 40–48% at about 1150°C and 0·001 s^− 1.     

Stress-strain properties of structural steel at strain rates of up to 105 per second at sub-zero,room and high temperatures

A testing technique and method of processing the displacement-time data have been developed following which the stress-strain characteristics of structural steel at strain rates between 10³ to 10⁵ per second over a strain of about 50% and at different temperatures have been determined. The steel under present test condition within this strain rate range showed a strong strain rate sensitivity. The material inertia and temperature rise during high speed deformation were found to have mutually cancelling effect on the deduced flow stress. In determining the results, appropriate friction correction was also made and the results presented in this paper are all converted to those under frictionless condition. Finally, a constitutive equation has been proposed for the steel incorporating the effects of work-hardening and strain rate sensitivity of the material.     

Low temperature and strain rate dependence of fracture stress and fracture toughness on thin Fe40Ni40B20 amorphous ribbon

The fracture stress and the critical stress intensity factor of the Fe₄₀Ni₄₀B₂₀ amorphous metallic ribbons 20 μm thick were measured in the temperature range 4.2–300 K and at deformation rates from 3.3×10⁻⁶ to 1.25×10⁻³ m⁻¹ with the aim to obtain more information on the condition for the onset and development of the inhomogeneous plastic deformation and fracture.     

Localized shear in sheet materials

Procedures and results of numerical simulations and experimental investigations of sheet materials under localized plastic deformation in shear are presented. Under dynamic loading these materials are considered to be viscoelastoplastic solids. Localized deformation and stress-strain distributions resulting from plastic shear are examined as a one-dimensional problem with account for nonlinear viscosity, damage, and temperature effects. Mild steel and high-strength aluminum alloy strips were tested under multiple impact loading with a small strain increment per impact (which corresponds to isothermal loading with sufficient accuracy). The experimental relations of localized shear deformation under such loading allow one to make the conclusion of a prevailing stress concentration effect on the kinetics of localized shear at the edge of the strip. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 5, pp. 53–63, September–October, 1999.     

Sliding wear properties of high purity copper in cryogenic environment

In an effort to understand the influence of cryogenic environment on the friction and wear properties of metallic materials, we performed a series of experiments on high purity work hardened copper (Cu) samples in liquid nitrogen (LN₂) environment against steel (bearing grade; SAE 52100) at varying loads and sliding speeds. The load was varied between 10 and 20 N and sliding speed was varied between 0.89 and 1.34 m/s. In our experiments, a reduction in the steady state coefficient of friction (μ_F) was noted with increasing load (10, 15, 20 N) at the highest sliding speed of 1.34 m/s. High wear rate of the order of 10⁻⁴ mm³/Nm was recorded, which was found to be independent of the load/sliding speed. On the basis of the experimental data and the characteristics of the worn surfaces it is confirmed that significant damage accumulation and plowing-induced material removal contribute to the wear losses. It is noteworthy that oxidative wear or mechanically mixed layer (no transfer from steel counter-body) did not occur to any significant extent under the chosen sliding conditions. The characteristics of the wear damage as a result of cryogenic sliding have been discussed with reference to the prevailing stress conditions and contact temperature.     

Effect of transient change in strain rate on plastic flow behaviour of low carbon steel

Plastic flow behaviour of low carbon steel has been studied at room temperature during tensile deformation by varying the initial strain rate of 3·3 × 10⁻⁴s⁻¹ to a final strain rate ranging from 1·33 × 10⁻³s⁻¹ to 2 × 10⁻³s⁻¹ at a fixed engineering strain of 12%. Haasen plot revealed that the mobile dislocation density remained almost invariant at the juncture where there was a sudden increase in stress with a change in strain rate and the plastic flow was solely dependent on the velocity of mobile dislocations. In that critical regime, the variation of stress with time was fitted with a Boltzmann type Sigmoid function. The increase in stress was found to increase with final strain rate and the time elapsed in attaining these stress values showed a decreasing trend. Both of these parameters saturated asymptotically at a higher final strain rate.