Damage to thick steel sheet in cyclic plastic flexure

The laminar development of damage in thick 10Г2С1 steel sheet during cold plastic deformation by cyclic flexure is investigated. The steel is subjected to pure flexure in a symmetric cycle, with strain of amplitude 5.5%. The variation in steel strength indicates the damage kinetics in the plastic deformation. In the region of reversible damage, the rate of change in the strength increases to a maximum and then declines. In the region of irreversible damage there is no further change in strength of steel before failure occurs. An upper limit is proposed for the damage of the steel: 20–30% of N_f, where N_f is the number of cycles to failure in cyclic extension–compression. In structural terms, the upper limit of reversible damage is assumed to correspond to the transformation of cellular dislocation structure to band structure.     

Dislocation emission and fatigue crack growth threshold

The stress intensity range ΔK below which no cyclic plastic deformation at the crack tip, and hence, no fatigue crack propagation occurs is investigated. The emission of dislocations from the crack tip is assumed as mechanism for the dislocation generation. For a mode III crack, a computer simulation is carried out to study the influence of the number of dislocations, the friction stress and the critical stress intensity, k_e, to emit a dislocation. If during loading only one dislocation is emitted, the return of this dislocation to the crack tip and the emission of a dislocation with an opposite sign and the recombination with the first dislocation are possible during unloading. The ΔK necessary for both mechanisms is about 2k_e. If during loading more than one dislocation is emitted, during unloading at first a certain number of disclocations return to the crack tip before a dislocation of opposite sign is emitted. The necessary ΔK to move one dislocation back to the crack tip during unloading decreases with increasing number of dislocations and reaches a constant values of about 1.1k_e. This value of ΔK then is roughly independent of the friction stress and k_e.     

A physical approach to the toughness problem: From thermodynamics to kinetics—I. The homogeneous case

The classical equilibrium equation of a crack under stress is reconsidered, introducing the deformation kinetics through a blunting correction to the elastic energy storage term, and a recalculation of the energy dissipation in the plastic zone. Both are expressed in terms of yield stress, strain hardening rate and strain rate sensitivity. The resulting instability criterion exhibits a ductile-brittle transition, and shows the influence of the above physical parameters on the critical stress intensity factor K_C. In addition, the blunting approximation, which neglects the energy dissipation in the plastic zone, is shown to be valid in most cases.     

KIC Modelling for a critical strain criterion involving the stress triaxiality effect

An analytical model for predicting fracture toughness K_IC is proposed based on a stress-modified critical strain criterion, that reflects the effect of stress triaxiality on ductile fracture. For K_IC modelling, the notch-tip strain and stress state are given by introducing asingular field for the case of power-law-hardening materials. Notch fracture toughness is interpreted in terms of the notch-root radius (ϱ): K_IC is predicted to increase with increasing ϱ, but has a minimum at a small ϱ. The microstructuralls characteristics distance and the reference critical strain can be estimated by fitting the K_IC vs ϱ data on the model equation. Finally, previous notch fracture-toughness data are re-analyzed with the proposed model: the current analysis explains well the interaction effect between the notch-tip strain field and the local-fracture-controlling microstructure even in the small ϱ range.     

Effects of plastic anisotropy and yield surface shape on sheet metal stretchability

The influence of plastic anisotropy and the shape of the yield surface on localized necking of thin metal sheets is examined. Forming limit curves (FLCs) of strain hardening, rate-sensitive sheets including Ti alloys, Al alloys, and steels are calculated on the basis of the Marciniak-Kuczynski approach using the quadratic Hill or the Drucker yield function in conjunction with either the flow or deformation theory of plasticity. The roles of the R-value and the yield surface shape in biaxial stretchability of sheet metals are delineated and discussed in relation to the plasticity theories and yield functions. It is concluded that the limit strains decrease with increasing R-value in the ε₂ > 0 region of an FLC but increase with the R-value in the ε₂ 0 region, and are independent of the R-value at plane strain conditions. These mixed, strain-path dependent effects are explained in terms of the shape of the yield surface and a recently proposed critical thickness strain criterion.     

Crack growth for the double slip plane crack model-I. The R-curve

The double slip plane (DSP) crack model of Weertman, Lin and Thomson has been used to obtain crack growth equations for the mode II or III crack under a monotonically increasing stress (the R-curve) in this paper. [In a companion paper the growth under cyclic stress (the Paris fatigue crack growth equation) is determined.] The success of the analysis depends upon the fact that the DSP crack closely approximates a Bilby-Cottrell-Swinden (BCS) crack when the slip zone is large compared with the slip plane to crack plane spacing. Consequently the dislocation distribution on the slip planes approximates the BCS crack one ahead of the crack tip. Behind the crack tip a result fortuitous for the analysis is found that the gradient of the dislocation density on a slip plane is proportional to the shear stress on the slip plane. The results obtained are: if the friction stress on a slip plane is constant the crack never propagates catastrophically. Instead crack extension occurs which is proportional to K² where rK is the stress intensity factor. Were the surface energy of a solid to be suddenly reduced, as it might be by the sudden introduction of an active environment, the distance the tip of a stressed stationary crack jumps is proportional to K. The distance jumped, for a large drop in surface energy, is smaller than the crack advance that occurs if the active environment were always present and the crack is monotonically loaded to the same value of K. If work hardening of the friction stress takes place stable crack growth takes place up to a critical K_c value. The R-curve equation is given by an integral which is simple in form but requires a numerical integration or series expansion. The critical K_c value is proportional to the critical K_cb stress intensity factor of a Griffith crack raised to the power (m + 1 )/2m where m is the power exponent of the simulated plastic stress-strain curve. We believe that this paper demonstrates the double slip plane crack model is the first crack model since the Griffith crack model and its variants that can give an explicit fracture equation starting from first principles.     

The shape memory effect and pseudoelasticity in polycrystalline Cu-Zn alloys

The shape memory effect associated with the reverse transformation of deformed martensite, pseudoelastic behavior involved in stress-induced martensite formation and the reversion of strained martensite after an applied stress is relaxed aboveA _f have been studied. Grain size and specimen geometry effects have been related to the above phenomena. Although recoverable strains as high as 10.85 pct were observed in coarse-grained (“bamboo” type) specimens, the shape memory effect is restricted in fine-grained specimens because of permanent grain boundary deformation and intergranular fracture which occurs at relatively low strains. A fine grain size also acts to suppress pseudoelastic behavior because permanent, localized deformation is generated concurrent with the formation of stress-induced martensite which inhibits reversion of the latter upon release of stress. The apparent plastic deformation of martensite belowM _f can be restored by transforming back to the original parent phase by heating toA _f (shape memory) or alternatively, can be recovered belowM _f by applying a small stress of opposite sign. Martensite deformed belowM _f with the same stress maintained while heating persists aboveA _f, but reverts to the parent phase in a pseudoelastic manner when the stress is relieved. The athermal thermoelastic martensite, which forms in groups composed of four martensite plate variants, undergoes several morphology changes under deformation. One of the variants within a plate group cluster may grow with respect to the others, and eventually form a single crystalline martensitic region. At a later stage pink colored deformation bands form in the same area and join up with increasing stress, resulting in thermally irreversible kinks. The clusters of plate groups may expand like grain growth or contract as a whole during deformation, or act as immobile “subgrains” which lead to permanent deformation at their boundaries. Stress-induced martensite usually forms as one variant of parallel plates which join up with increasing stress to form single crystalline regions. Further stress leads to pink colored deformation bands, similar to those in the deformed athermal martensite. Other similarities and differences between the stress-induced and athermal martensite have been investigated and are discussed.     

Determining the brittle strength and mechanical stability of structural steel

The relation of the brittle strength and mechanical stability of structural steel to the basic mechanical characteristics σ_0.2, σ_B, and ψ_f in above-uniform plastic deformation is considered. The relations between the equivalent strain e _equ and the characteristics of strain hardening (individually or in combination) in the region of nonuniform plastic deformation are established. On that basis, the brittle strength R _MC and mechanical stability K _ms of structural steel may be predicted in the range from ?196 to 20°C. The temperature dependence of these relationships is established. Calculated values of R _MC and K _ms are presented for some structural steels and weld seams in different groups, and the accuracy of the method is estimated. The formulas obtained are the same for different combinations of the strength and plastic properties of the structural steels and for different heat-treatment conditions.     

Effect of aging treatments on the fatigue crack growth and threshold behavior of AA 2219 aluminium alloy

The fatigue crack growth and threshold behavior of AA2219 Al-alloy has been examined for naturally aged (NA), under aged (UA), peak aged (PA) and over aged (OA) conditions. Significant differences were observed in the fatigue crack growth at low and high stress intensity ranges. The alloy in the NA condition possesses the highest resistance to fatigue crack initiation which can be viewed from the values of achieved threshold stress intensity range, ΔK _TH . In the intermediate ΔK (Paris law) regime, all the four materials fall into a single band. In the high ΔK regime (> 20 MPa√m) PA condition exhibits better crack growth resistance than under aged conditions. The inhomogeneous transcrystalline slip in the UA condition results in the slower crack growth at low ΔK. The fracture morphology changes from crystallographic facets in the threshold region to clearly developed ductile striations in the Paris law regime to microvoid coalescence in the high ΔK region.     

Fatigue Strength and Crack Initiation Mechanism of Very-High-Cycle Fatigue for Low Alloy Steels

The fatigue strength and crack initiation mechanisms of very-high-cycle fatigue (VHCF) for two low alloy steels were investigated. Rotary bending tests at 52.5?Hz with hour-glass type specimens were carried out to obtain the fatigue propensity of the test steels, for which the failure occurred up to the VHCF regime of 10⁸ cycles with the S-N curves of stepwise tendency. Fractography observations show that the crack initiation of VHCF is at subsurface inclusion with ??fish-eye?? pattern. The fish-eye is of equiaxed shape and tends to tangent the specimen surface. The size of the fish-eye becomes large with the increasing depth of related inclusion from the surface. The fish-eye crack grows faster outward to the specimen surface than inward. The values of the stress intensity factor (K _I ) at different regions of fracture surface were calculated, indicating that the K _I value of fish-eye crack is close to the value of relevant fatigue threshold (??K _th ). A new parameter was proposed to interpret the competition mechanism of fatigue crack initiation at the specimen surface or at the subsurface. The simulation results indicate that large inclusion size, small grain size, and high strength of material will promote fatigue crack initiation at the specimen subsurface, which are in agreement with experimental observations.     

On the unity of various fatigue processes

Some concepts of the relation between the fatigue life during low-cycle and high-cycle fatigue are presented. Fatigue is shown to be the accumulation of a certain sum of damages in plastic deformation cycles at stress range Δ?_pl. The accumulation during low-cycle fatigue occurs in the entire volume of a sample, and that during high-cycle fatigue occurs only in the plastic zone of a growing crack. As follows from the constancy of the sum of damages, crack motion per cycle w is a fraction w/r _s = const of the plastic zone size r _s ～ K _I ² at stress intensity K _I. Therefore, Paris’ law w ～ K _I ² for high-cycle fatigue results from the Coffin relationship n ～ 1/(Δ?_p)² for fatigue life n during low-cycle fatigue. Paris’ law is a self-similar solution of the second kind, where scaling follows from the solution to a nonlinear problem for the eigenvalue of w(r _s ). The scale invariance is caused by the self-similarity of the fields near a crack edge. The subsurface layer several grains in depth in a material with yield stress σ _s flows at stress σ _s /2. Low-cycle crack nucleation in this layer causes the level σ_?1 ≈ σ _s /2 of the high-cycle fatigue limit of smooth samples. Giga-cycle fatigue at σ < σ _s /2 is controlled by concentrators in the structure volume rather than at the surface.     

Residual stress induced fracture in glass-sapphire composites: planar geometry

Cracking resulting from thermal expansion mismatch generated residual stresses is investigated using a model system consisting of bonded layers of sapphire and borosilicate glass. Three planar geometries are employed; a bilayer configuration and two sandwich configurations. The bilayer configuration of a thin sapphire sheet bonded to a thick glass substrate models the cracking due to a thin film under residual tension. The cracks formed adopt a characteristic shape running parallel to the planar interface and at a depth consistent with recent predictions of Suo and Hutschinson for a K_II = 0 steady-state propagation trajectory. The same result is obtained with a novel test sample consisting of a sapphire sheet bonded to a triangular shaped substrate. The other two configurations, of a glass block sandwiched between two sapphire sheets and of a sapphire sheet between two glass blocks, enable the residual stress cracking to be explored for conditions under which no net bending moment exists.     

A Deformation Mechanism Map for the 1.23Cr-1.2Mo-0.26V Rotor Steel and Its Verification Using Neural Networks

A deformation mechanism map is constructed for the 1.23Cr-1.2Mo-0.26V rotor steel as a function of temperature, stress, and strain rate using published creep test results and the current understanding of time dependent deformation mechanisms operative in complex engineering alloys. Instead of diffusional creep, grain boundary sliding (GBS) accommodated by different deformation processes is considered dominant at lower strain rates. The GBS dominated region is further sub-divided into two parts, where GBS is accommodated by wedge type cracking at temperatures below 0.5T/T _m and the accommodation process changes to creep cavitation at temperatures above 0.5T/T _m. The map is verified using experimental data and artificial neural network modeling. The proposed artificial neural network model is capable of predicting the dominance of different deformation mechanisms in 1.23Cr-1.2Mo-0.26V steel over a wide range of stress and temperature. This modeling procedure can potentially be used to construct or expand deformation mechanism maps for other engineering alloys.     

Austenite flow stress behaviour during continuous cooling through the metastable austenite region

Studies of the austenite flow stress during cooling have revealed changes in the flow stress behaviour as the temperature decreases from the single phase austenite region into the metastable region. This suggests that the onset of metastability is associated with a change in the microstructure even though, in the metastable temperature region (i.e. between the equilibrium austenite-to-ferrite transformation temperature, Ae₃, and the non-equilibrium transformation start temperature, the Ar₃), austenite has yet to transform to ferrite. Several steel compositions with different Ae₃ temperatures were first subjected to continuous deformation by compression during cooling to follow the variations in flow stress with temperature. In these tests, the metastable region appeared to be associated with an increase in the rate of increase in flow stress with decreasing temperature. Neutron diffractometry at high temperatures was used to monitor any crystallographic changes associated with the metastable region. The results of the latter indicate a faster rate of contraction of the austenite lattice as the temperature decreases through the metastable state, compared with that observed as the temperature decreases through the stable austenite region. The possible relationship between this observation and the flow stress behaviour will be addressed in this paper.     

Effect of strain rate and temperature on the flow stress of β-phase titanium- hydrogen alloys

Compression tests were carried out on seven titanium-hydrogen alloys containing hydrogen concen-trations up to 31 at. pct. All the experiments were performed within the β-phase field at strain rates of 0.001 to 1.0s ^~1 The dependences of the steady-state flow stress on strain rate, temperature, and hydrogen concentration were determined. The strain rate sensitivity increases with temperature but decreases with hydrogen concentration. The experimental activation energy of deformation decreases when the flow stress or strain rate is increased. At a fixed strain rate, it decreases when the hydrogen concentration is increased. However, when measured at a fixed steady-state stress, the activation energies are nearly the same for all the alloys. The steady-state flow stress increases with hydrogen concentration as can be expressed by both linear and quadratic dependences. The flow behavior of the alloys can also be described in terms of thermally activated glide and the relation $$\dot \varepsilon = K\sigma ^4 \exp \left( { - \frac{{\Delta H_0 }}{{kT}}} \right)\exp \left( {\frac{{v\sigma }}{{kT}}} \right)$$ where the constantsv and ΔH₀ are independent of hydrogen concentration, while the parameterK decreases exponentially when the hydrogen concentration is increased.     

Effect of mean stress on hydrogen assisted fatique crack propagation in duplex stainless steel

Hydrogen assisted subcritical cleavage of the ferrite matrix occurs during fatigue of a duplex stainless steel in gaseous hydrogen. The ferrite fails by a cyclic cleavage mechanism and fatigue crack growth rates are independent of frequency between 0.1 and 5 Hz. Macroscopic crack growth rates are controlled by the fraction of ferrite grains cleaving along the crack front, which can be related to the maximum stress intensity, K_max. A superposition model is developed to predict simultaneously the effects of stress intensity range (ΔK) and K ratio (K_min/K_max). The effect of K_max is rationalised by a local cleavage criterion which requires a critical tensile stress, normal to the {001} cleavage plane, acting over a critical distance within an embrittled zone at the crack tip.     

Analysis of softening alloys of the Al-Ni system containing particles of variable dispersity

Regularities of the deformation strengthening and softening of aluminum alloys containing second-phase Al₃Ni particles 0.3 to 2.2 μm in size with a volume fraction from 0.03 to 0.1 are investigated during cold deformation and subsequent annealing at 0.6t _m. It is shown that the largest hardness increment is observed for alloys with a maximal fraction of fine particles (d = 0.3 μm) after rolling deformation larger than 0.4. Fine particles prevent the development of crystallization upon true deformation up to 2.3, thereby effectively inhibiting softening. An increase in the particle size to 1.2–2.2 μm stimulates nucleation during recrystallization, substantially accelerating this process. For example, in order to ensure recrystallization uniformly over the entire sheet volume at d = 2.2 μm, cold deformation with ? = 0.4 is sufficient.     

A rationalisation of fatigue thresholds in pearlitic steels using a theoretical model

From a detailed re-examination of results in the literature, the effects of microstructure sizes, namely interlamellar spacing, pearlitic colony size and the prior austentitic grain size on the thresholds for fatigue crack growth (ΔK_th) and crack closure (K_{cl, th}) have been illustrated. It is shown that while interlamellar spacing explicitly controls yield strength, a similar effect on ΔK_th cannot be expected. On the other hand, the pearlitic colony size is shown to strongly influence ΔK_th and K_{cl, th} through the deflection and retardation of cracks at colony boundaries. Consequently, an increase in ΔK_th and K_{cl, th} with colony size has been found. The development of a theoretical model to illustrate the effects of colony size, shear flow stress in the slip band and macroscopic yield strength on K_{cl, th} and ΔK_th is presented. the model assumes colony boundaries as potential sites for slip band pile-up formation and subsequent crack deflection finally leading to zig-zag crack growth. Using the concepts of roughness induced crack closure, the magnitude of K_{cl, th} is quantified as a function of colony size. In deriving the model, the flow stress in the slip band has been considered to represent the work hardened state in pearlite. Comparison of the theoretically predicted trend with the experimental data demonstrates very good agreement. Further, the intrinsic or closure free component of the fatigue threshold, ΔK_{eff, th} is found to be insensitive to colony size and interlamellar spacing. Using a criterion for intrinsic fatigue threshold which considers the attainment of a critical fracture stress over a characteristic distance corresponding to interlamellar spacing, ΔK_th values at high R values can be estimated with reasonable accuracy. The magnitude of ΔK_th as a function of colony size is then obtained by summing up the average value of experimentally obtained ΔK_{eff, th} values and the predicted K_{cl, th} values as a function of colony size. Again, very good agreement of the theoretically predicted ΔK_th values with those experimentally obtained has been demonstrated.