A new model for the volume fraction of martensitic transformations

A model using an energy balance is proposed to describe the volume fraction of multiple-interface martensitic transformations. For martensitic transformations without external stresses at quenching temperature T<M _s , the volume fraction of martensite (ξ) is proportional to the undercooling (M _s −T) and inversely proportional to a linear function of the quenching temperature (T); thus, ξ=(M _s −T)/[M _s −βM _f −(1−β)T], where β is a material constant. For stress-induced martensitic transformations under stress σ _ik ^a with temperature T>M _s , the relationship is ξ = ξ₀[1 - λ _ik ^σ (σ _ik ^Ms ]^-1, where ξ ₀ is the initial detectable amount of martensite formed at martensitic starting stress σ _ik ^Ms and λ _ik ^σ is a material constant. It is found that the results obtained from this model are in good agreement with experimental results.     

Orientation dependence of β1 → β1′ stress-induced martensitic transformation in a Cu-AI-Ni alloy

A systematic investigation was carried out to settle some critical issues on the orientation dependence of the stress-induced martensitic transformation. The transformation we picked up is the β_l (DO3) → β₁′ (18R) stress-induced transformation in a Cu-14.1 mass pct Al-3.9 mass pct Ni alloy. By utilizing tensile tests and two surface analyses coupled with X-ray diffraction, the following clear results were obtained. Concerning the variant selection rule under stress, it was found to be the shape strain which interacts with an applied stress. The critical resolved shear stress for the martensitic transformation was found to have orientation dependence, the shear stress increasing with the normal stress. The observed transformation strains were consistent with those calculated from the shape strain in all orientations. The strong orientation dependence of the Young’s modulus was consistent with that predicted by the elastic constants in the parent phase.     

Internal stresses and structures developed during creep

Specimens of 304 stainless steel subjected to different thermomechanical histories develop different internal stresses, σ _i , and different substructures. Creep rate is uniquely related not to the applied stress, σ _A , but to the effective stress, σ^*=(σ _A −σ _i ). Values of σ^* are determined from experimental results and σ _i calculated from σ _i =(σ _A −σ^*). Results show σ _i increases with the applied stress according to σ _i ∝σ _A ^1.7 . Transmission electron microscopic observations show that the density of dislocations within subgrains, ϱ _D , and the subgrain diameter,D, vary with applied stress according to: ϱ _D ∝σ _A ^K ,D ∝ σ _A ^−0.8 , whereK=1.4 to 2.0. Subgrain misorientation is independent of creep stress, strain, or temperature. The contributions of these structural variables to the internal stress are discussed.     

Size effects on the microscopic cleavage fracture stress, σ F * , in martensitic microstructures

Effects of testpiece size on the microscopic cleavage fracture stress, σ_F*, have been investigated for as-transformed, autotempered martensitic microstructures, by employing geometrically similar (scaled) testpieces. Both fine- and coarse-grained martensites have been examined. For a coarsegrained martensitic microstructure, significant effects on cr* attributable to sampling volume have been observed,i.e., reduced values of σ_F* are obtained as the testpiece size is increased. For a fine-grained martensitic microstructure the effects on σ_F* attributable to sampling volume are reduced, but significant reductions in σ_F* occur due to the lack of depth hardenability in large testpieces. The values of σ_F* observed are consistent with a micromechanism of failure involving the propagation of microcracks from autotempered carbides. For the coarse-grained condition the most potent autotempered carbides lie on embrittled prior austenite grain boundaries.     

Microstructural effects on the cleavage fracture stress of fully pearlitic eutectoid steel

The microstructural parameter(s) controlling the critical cleavage fracture stress, σ_F, of fully pearlitic eutectoid steel have been investigated. Independent variation of the pearlite interlamellar spacing,S _p, and the prior austenite grain size were accomplished through heat treatment. Critical cleavage fracture stresses were measured on bluntly-notched bend specimens tested over the temperature range -125 °C to 23 °C. The cleavage fracture stress increased with decreasingS _p, and was independent of prior austenite grain size. Fine pearlitic microstructures exhibited temperature, strain-rate, and notched-bar geometry independent values for σ_F, consistent with propagation-controlled cleavage fracture. Coarse pearlitic specimens exhibited temperature-dependent values for σ_F over a similar temperature range. Inclusion-initiated fractures were generally located at or beyond the location of the peak normal stress in the bend bar, while cracking associated with pearlite colonies was observed to be closer to the notch than the predicted peak stress location. The calculated values for σ_F were independent of both the type and location of initiation site(e. g., inclusion, pearlite colony). Thus, although inclusions may provide potent fracture initiation sites, their presence or absence does not necessarily change σ_F in fully pearlitic microstructures. formerly Graduate Student, Carnegie Mellon University     

Transformation behavior of TRIP steels

True-stress (σ), true-strain (ε) and volume fraction martensite(f) were measured during both uniform and localized flow as a function of temperature on TRIP steels in both the solution-treated and warm-rolled conditions. The transformation curves(f vs ε) of materials in both conditions have a sigmoidal shape at temperatures above M_s ^σ (maximum temperature at which transformation is induced by elastic stress) but approach initially linear behavior at temperatures below M_s ^σ where the flow is controlled by transformation plasticity. The martensite which forms spontaneously on cooling or by stress-assisted transformation below M_s ^σ exhibits a plate morphology. Additional martensite units produced by strain-induced nucleation at shear-band intersections become important above M_s ^σ. Comparison of σ-ε andf-ε curves indicate that a “rule of mixtures” relation based on the “static” strengthening effect of the transformation product describes the plastic flow behavior reasonably well above M_s ^σ, but there is also a dynamic “transformation softening” contribution which becomes dominant below M_s ^σ due to the operation of transformation plasticity as a deformation mechanism. Temperature sensitivity of the transformation kinetics and associated flow behavior is greatest above M_s ^σ. Less temperature-sensitive TRIP steels could be obtained by designing alloys to operate with optimum mechanical properties below M_s ^σ.     

Microstructural dependence of Fe-high Mn tensile behavior

The tensile properties of Fe-high Mn (16 to 36 wt pct Mn) binary alloys were examined in detail at temperatures from 77 to 553 K. The Mn content dependence of the deformation and fracture behavior in this alloy system has been clarified by placing special emphasis on the starting microstructure and its change during deformation. In general, the intrusion of hcp epsilon martensite (ε) into austenite (γ) significantly increases the work hardening rate in these alloys by creating strong barriers to further plastic flow. Due to the resulting high work hardening rates, large amounts of e lead to high flow stresses and low ductility. Alloys of 16 to 20 wt pct Mn are of particular interest. While these alloys are thermally stable with respect to bcc α’ martensite formation, 16 to 20 wt pct Mn alloys undergo a deformation induced ε →α’ transformation. The martensitic transformation plays two contrasting roles. The stress-induced ε→ α’ transformation decreases the initial work hardening rate by reducing locally high internal stress. However, the work hardening rate increases as the accumulated α’ laths become obstacles against succeeding plastic flow. These rather complicated microstructural effects result in a stress-strain curve of anomolous shape. Since both the M_s and M_d temperatures for both the ε and α’-martensite transformations are strongly dependent on the Mn content, characteristic relationships between the tensile behavior and the Mn content of each alloy are observed.     

Critical assessment of the local cleavage stress σ ƒ * in notch specimens of C-Mn steel

An elastic-plastic finite element method (FEM) was used to calculate the stress and strain distributions ahead of notches with various root radii in a bending specimen of C-Mn steel with grain sizes of 10 and 30 μm. By accurately measuring the distance of the cleavage initiation site from the root of the notch, the local cleavage stress σ _ƒ ^* was measured. When the notch radius increased from 0.25 to 1.0 mm, the distribution of high stress had a definite variation but the σ _ƒ ^* remained relatively constant. In notch specimens with different root radii, the critical fracture event is identical,i.e., propagation of a ferrite grain-sized crack into the neighboring matrix. Therefore, the σ _ƒ ^* is mainly determined by the length of the critical microcrack, here, the size of ferrite grain instead of the high stress volume for finding an eligible brittle particle. The critical strain for initiating a crack was about 1 pct. The cleavage site ahead of a notch was related to the relative distributions of stress and strain and the random distribution of the weakest grains. The higher fracture load of the fine-grain material can be attributed to its higher value of σ _ƒ ^* /σ_o as compared with the coarse-grain. The σ _ƒ ^* /σ_o is a potential engineering parameter for toughness assessment in notch specimens.     

Effect of internal stress on autocatalytic nucleation of martensitic transformation

On the basis of classical nucleation theory of martensitic transformation (MT), the effect of internal stress on autocatalytic nucleation of MT is quantitatively described. The complex stress field pictures outside a formed martensitic plate are first calculated through Eshelby’s theory, and then the interaction energies between the martensitic plate and embryos with 24 possible variants can be further obtained. Based on the calculation of interaction energy, the effect of internal stress on autocatalytic nucleation of MT and morphological characteristics of martensite are explained. In this investigation, two kinds of alloys—non-thermoelastic materials (e.g., Fe-30Ni) and thermoelastic materials (e.g., Cu-46.6Zn)—are studied, and their difference in autocatalytic nucleation and morphological characteristics of martensite are indicated.     

Pseudoelastic behavior of a CuAlNi single crystal under uniaxial loading

In order to study the basic properties of pseudoelasticity of a CuAlNi single crystal, an investigation was carried out to observe and analyze the orientation dependence of the stress-induced martensitic transformation. The transformation is the β ₁ to β′₁ stress-induced transformation in a Cu-13.7 pct Al-4.18 pct Ni (wt pct) alloy. From the uniaxial tension of three groups of differently oriented flat specimens, we obtained a series of stress-strain curves. In addition, the micrograph of martensitic evolution was observed by utilizing a long-focus microscope. It is found that martensite appears in the shape of bands or thin plates on the surface of the specimen. The formation of martensite is a very quick process, and martensite “jumps” out until the specimen is completely transformed into a single variant. The experimental results are analyzed and compared to a constitutive model proposed recently. It is found that the constitutive model cannot describe transformation hardening, since the model ignores the surface-energy change. Nevertheless, the proposed constitutive model cannot only precisely predict the forward and reverse transformation, but can also characterize the stress-strain hysteresis behavior during pseudoelastic deformation under uniaxial tension loading.     

Fatigue crack propagation in carburized X-2M steel

The growth rates of fatigue cracks propagating through the case and into the core have been studied for carburized X-2M steel (0.14 C, 4.91 Cr, 1.31 Mo, 1.34 W, 0.42 V). Fatigue cracks were propagated at constant stress intensities, ΔK, and also at a constant cyclic peak load, and the crack growth rates were observed to pass through a minimum value as the crack traversed the carburized case. The reduction in the crack propagation rates is ascribed to the compressive stresses which were developed in the case, and a pinched clothespin model is used to make an approximate calculation of the effects of internal stress on the crack propagation rates. We define an effective stress intensity, K_e = K_a + K_i, where K_a is the applied stress intensity, K_i = σ_id _i ^1/2 , σ_i is the internal stress, and d_i is a characteristic distance associated with the depth of the internal stress field. In our work, a value of d_i = 11 mm (0.43 inch) fits the data quite well. A good combination of resistance to fatigue crack propagation in the case and fracture toughness in the core can be achieved in carburized X-2M steel, suggesting that this material will be useful in heavy duty gears and in aircraft gas turbine mainshaft bearings operating under high hoop stresses.     

Thermal activation model of endurance limit

A thermal activation model of the endurance limit is proposed in the present study. It can quantitatively explain the effects of temperature and frequency on the endurance limit of metals at or below room temperature. Theoretical analysis indicates that the endurance limit, σ_ac, which is considered as a parameter characterizing the resistance of metals to cyclic microplastic deformation, has the same thermally activated nature as the plastic flow stress has and it can be resolved into two independent components: the long-range internal stress (the athermal component), μ(ε_apc), and the short-range effective stress (the thermal component), σ_a ^*(T, ε_p). The former is considered as a material constant insensitive to temperature and strain rate (or frequency). The latter, the temperature- and strain rate-dependent part of the endurance limit, is approximately identical with the effective stress component of plastic flow stress (or cyclic yielding stress). In light of the thermal activation model, the temperature and strain-rate dependence of monotonic and cyclic flow stresses in a low alloy steel (16Mn) and a precipitation-hardening aluminum alloy (LY12CZ) were experimentally investigated. The results indicate that the effective stress components of monotonic and cyclic flow stresses are identical, if the temperature and strain rate are held unchanged, and that both of them are approximately independent of the magnitude of plastic strain. On the basis of the thermal activation model, an expression predicting the endurance limit below room temperature is offered. The predicted values of the endurance limit agree with the test data of steels and aluminum alloys available in literature.     

Fatigue crack propagation in carburized high alloy bearing steels

Fatigue cracks were propagated through carburized cases in M-50NiL (0.1 C,4 Mo, 4 Cr, 1.3 V, 3.5 Ni) and CBS-1000M (0.1 C, 4.5 Mo, 1 Cr, 0.5 V, 3 Ni) steels at constant stress intensity ranges, ΔK, and at a constant cyclic peak load. Residual compressive stresses of the order of 140 MPa (20 Ksi) were developed in the M-50NiL cases, and in tests carried out at constant ΔK values it was observed that the fatigue crack propagation rates,da/dN, slowed significantly. In some tests, at constant peak loads, cracks were stopped in regions with high compressive stresses. The residual stresses in the cases in CBS-1000M steel were predominantly tensile, probably because of the presence of high retained austenite contents, andda/dN was accelerated in these cases. The effects of residual stress on the fatigue crack propagation rates are interpreted in terms of a pinched clothespin model in which the residual stresses introduce an internal stress intensity, K_i where K_i, = σ_id _i ^1/2 (σ_i = internal stress, d_i = characteristic distance associated with the internal stress distribution). The effective stress intensity becomes K_e = K_a + K_i where K_a is the applied stress intensity. Values of K_i were calculated as a function of distance from the surface using experimental measurements of σ_i and a value of d_i = 11 mm (0.43 inch). The resultant values of K_e were taken to be equivalent to effective ΔK values, andda/dN was determined at each point from experimental measurements of fatigue crack propagation obtained separately for the case and core materials. A reasonably good fit was obtained with data for crack growth at a constant ΔK and at a constant cyclic peak load. The carburized case depths were approximately 4 mm, and the possible effects associated with the propagation of short cracks were considered. The major effects were observed at crack lengths of about 2 mm, but the contributions of short crack phenomena were considered to be small in these experiments, since the two steels were at high strength levels, and short cracks would be expected to be of the order of 10 μm. Also, the two other steels behaved differently and in a way which followed the residual stress patterns. Both M-50NiL and CBS-1000M have a high fracture toughness, with K_lc = 50 MPa · m^1/2 (45 Ksi · in^1/2), and the carburized cases exhibit excellent resistance to rolling contact fatigue. Thus, M-50NiL, carburized, may be useful for bearings where high tensile hoop stresses are developed, since fatigue cracks are slowed in the case by the residual compressive stresses, and fracture is resisted by the relatively tough core.     

Computer simulation of martensitic transformations in constrained,two-dimensional crystals under external stress

This article reports a computer simulation study of the microstructures produced by martensitic transformations. In the present work, the transformation strain is dyadic, and the transformation is athermal and irreversible. The transformation occurs in a two-dimensional crystal that is constrained in a matrix that has no net transformation strain and may be subject to external stress. The crystal is divided into elementary cells. The transformation is simulated by computing the elastic strain energy in the linear elastic approximation and transforming the most-favored cell in each step to generate the minimum-energy transformation path. The simulation generates the microstructure at each step of the transformation and plots a temperature-transformation (TT) curve by computing the chemical driving force required to maintain the transformation and assuming that it is proportional to the undercooling. The results show that the matrix constraint causes complex, multivariant microstructures and separatesM _sandM _f. Multiple variants partly relax the shear part of transformation strain but interfere so that the transformation is difficult to maintain. The dilational part of the transformation strain produces interesting microstructures, such as “butterfly martensite,” in partially transformed crystals. It also increases ΔM since it produces a hydrostatic stress that cannot be compensated by mixing variants. The applied stress can be divided into hydrostatic and deviatoric components. The hydrostatic component changesM _swithout altering the microstructure or ΔM. The deviatoric stress changes the relative energies of the variants and produces a microstructure that is rich in the favored variant. It also increases ΔM, since single-variant transformations must be sustained against an accumulating, uncompensated shear. The thermal resistance (ΔM) increases with the magnitude of the deviatoric stress until a high-stress limit is reached and only one variant appears. The microstructure is most complex at intermediate stress, where both variants develop in a complex internal stress field. Cyclic stress dramatically increases the extent of transformation at given maximum load. The martensite that has already formed becomes a source of intense internal stress when the stress is reversed, promoting further transformation.     

Young’s modulus and mechanical properties of Ti-29Nb-13Ta-4.6Zr in relation to α″ martensite

An investigation on the formation of α″ martensite and its influence on Young’s modulus and mechanical properties of forged Ti-29Nb-13Ta-4.6Zr (wt pct) alloy is reported in this article. For ice-water-quenched specimens after solution treatment at 1023, 1123, and 1223 K in the single β-phase field for 1.8, 3.6, 14.4, and 28.8 ks, X-ray diffraction and internal friction measurements showed that the volume fraction of the α″ martensite changes with both solution temperature and time. This effect has been attributed mainly to the influence of grain size of the β-parent phase on the stability of the β phase and, consequently, on the martensitic start (M _s) temperature. A critical grain size of 40 μm was identified for the β phase, below which the martensitic transformation is largely suppressed because of low M _S temperature. With the β grain size increasing above this critical value, the volume fraction of the α″ martensite increases significantly at first and then decreases gradually with further grain growth. The α″ martensite was shown to possess good ductility and, compared to the β phase, lower strength and hardness but nearly identical Young’s modulus in the studied alloy.     

On the stress exponent and the rate-controlling mechanism of high-temperature creep in some solid solutions

The internal stress, σ_i, and the effective-stress exponent of the dislocation velocity,m*, have been determined during creep of Fe-3.5 at. pct Mo alloy at 1123 K under 10.8 to 39.2 MN/m² and of Ni-10.3 at. pct W alloy at 1173 K under 19.6 to 88.2 MN/m². Both alloys have been classified among class I alloys under a certain condition including the present one, because the applied-stress exponent of the steady-state creep rates,n, is almost 3. Values of σ_i obtained by stress-transient dip test were small and almost independent of the applied stress, σ_c, in Fe-3.5 Mo alloy. On the other hand, in Ni-10.3 W alloy σ_i increased with increasing σ_c as in the case of many pure metals. The value ofm* obtained by analyzing stress-relaxation curves immediately after creep deformation was unity in Fe-3.5 Mo alloy, whereas in Ni-10.3 W alloy it was about 2.5. These results indicate that the rate-controlling mechanisms in creep are different from each other in these two alloys and that the classification according ton-value does not always coincide with the classification according to the rate-controlling mechanisms. It is concluded that the fact thatn ≃ 3 is not a sufficient evidence supporting that creep is controlled by one of microcreep mechanisms.     

The strain dependence of the flow stress-grain size relation for 70:30 brass

The grain size dependence of the stress-strain behavior of annealed 70:30 brass was evaluated using room temperature tensile tests. The resulting data, which covered × 10^-5 to 4 × 10^-1, were analyzed in terms of the conventional Hall-Petch stress-grain size equation, σ_∈ = σ_O∈ +k∈l-1/2, and, also, in terms of the extended Hall-Petch equation previously proposed for 70:30 brass, σ_є = σ0y+ A Є _p + β(є _p /l ^1/2 +kl ^−1/2 The lattice friction stress, σ0_∈, increased linearly with plastic strain over nearly the full strain range. The lattice friction stress for the initiation of plastic flow, σ0_y, was evaluated using two alternative double extrapolation procedures. Both extrapolation techniques, which involved the macrostrain behavior, gave the same σ0_y value of 3.4 kg/mm², which agreed with the σ0_∈ value determined directly in the microstrain region (∈ <-10^-3). Large grain size specimens, which yielded homogeneously, exhibited a kx2208; value of only 0.2 kg/mm^3/2 at a plastic strain of 1 × 10^-5; however this small kx2208; increased rapidly with increasing microstrain. For the small grain size specimens, which yielded via a Luders extension,kε was essentially constant at 0.8 kg/mm^3/2 for all microstrains; however, kx03B5; did increase in the macrostrain region to a maximum value of 1.6 kg/mm^3/2. When consideration was given to a grain size dependent increase in dislocation density, an intrinsic grain boundary resistance to plastic flow of approximately 0.7 kg/mm^3/2 was obtained. This paper is based upon a thesis submitted by W. L. Phillips in partial fulfillment of the requirements of the degree of Doctor of Philosophy at University of Maryland.     

Stress-assisted isothermal martensitic transformation: Application to TRIP steels

Low-temperature plastic flow in TRIP steels has been found to be controlled by stress-assisted isothermal martensitic transformation. For these conditions, the thermodynamics and kinetic theory of martensitic transformations leads directly to constitutive relations predicting the dependence of flow stress on temperature, strain, strain-rate, and stress-state, consistent with the observed behavior of TRIP steels. Guidelines are obtained for the control of temperature sensitivity, σ -ɛ curve shape, and stress-state effects to achieve novel mechanical properties.