The shear fracture of dual-phase steel

Unexpected fractures at high-curvature die radii in sheet forming operations limit the adoption of advanced high strength steels (AHSS) that otherwise offer remarkable combinations of high strength and tensile ductility. Identified as “shear fractures” or “shear failures,” these often show little sign of through-thickness localization and are not predicted by standard industrial simulations and forming limit diagrams. To understand the origins of shear failure and improve its prediction, a new displacement-controlled draw-bending test was developed, carried out, and simulated using a coupled thermo-mechanical finite element model. The model incorporates 3D solid elements and a novel constitutive law taking into account the effects of strain, strain rate, and temperature on flow stress. The simulation results were compared with companion draw-bend tests for three grades of dual-phase (DP) steel over a range of process conditions. Shear failures were accurately predicted without resorting to damage mechanics, but less satisfactorily for DP 980 steel. Deformation-induced heating has a dominant effect on the occurrence of shear failure in these alloys because of the large energy dissipated and the sensitivity of strain hardening to temperature increases of the order of 75 °C. Isothermal simulations greatly overestimated the formability and the critical bending ratio for shear failures, thus accounting for the dominant effect leading to the inability of current industrial methods to predict forming performance accurately. Use of shell elements (similar to industrial practice) contributes to the prediction error, and fracture (as opposed to strain localization) contributes for higher-strength alloys, particularly for transverse direction tests. The results illustrate the pitfall of using low-rate, isothermal, small-curvature forming limit measurements and simulations to predict the failure of high-rate, quasi-adiabatic, large-curvature industrial forming operations of AHSS.     

Numerical simulations of necking during tensile deformation of aluminum single crystals

Finite element simulations are used to study strain localization during uniaxial tensile straining of a single crystal with properties representative of pure Al. The crystal is modeled using a constitutive equation incorporating self- and latent-hardening. The simulations are used to investigate the influence of the initial orientation of the loading axis relative to the crystal, as well as the hardening and strain rate sensitivity of the crystal on the strain to localization. We find that (i) the specimen fails by diffuse necking for strain rate exponents m < 100, and a sharp neck for m > 100. (ii) The strain to localization is a decreasing function of m for m < 100, and is relatively insensitive to m for m > 100. (iii) The strain to localization is a minimum when the tensile axis is close to (but not exactly parallel to) a high symmetry direction such as [1 0 0] or [1 1 1] and the variation of the strain to localization with orientation is highly sensitive to the strain rate exponent and latent-hardening behavior of the crystal. This behavior can be explained in terms of changes in the active slip systems as the initial orientation of the crystal is varied.     

Effect of γ − α′ phase transformation on plastic adaptation to cyclic loads at cryogenic temperatures

Metastable, type FCC metals and alloys are often applied at extremely low temperatures because of their excellent ductility over the whole temperature range practically down to the absolute zero. These materials (like stainless steels) are frequently characterised by the low stacking fault energy and undergo at low temperatures the plastic strain induced transformation from the parent phase “γ” to the secondary phase “α′”. The phase transformation process consists in creation of two-phase continuum, where the parent phase coexists with the inclusions of secondary phase in thermodynamic equilibrium. The evolution of material micro-structure induces strain hardening related to interaction of dislocations with the inclusions and to increase of equivalent tangent stiffness as a result of evolving proportions of both phases, each characterised by different stiffness. The corresponding hardening model is based on micromechanics and on the Hill concept (1965) supplemented by Mori and Tanaka (1973) homogenisation scheme. Identification of parameters of the constitutive model has been carried out for 304L and 316L stainless steels, based on the available experimental data. The model has been used to describe phase transformation in rectangular beams, circular rods and thin-walled shells subjected to cyclic loads at cryogenic temperatures. Moreover, non-proportional loading paths were studied. A new feature of structures made of metastable materials has been observed. As soon as the γ ? α′ phase transformation begins, the evolution of material micro-structure accelerates the process of adaptation of structural member to cyclic loads and enhances therefore its fatigue life when compared to classical elastic–plastic structures.     

Deformation behavior and microstructure/texture evolution of an annealed 304 AISI stainless steel sheet. Experimental and micromechanical modeling

Different tensile tests are performed at −60 °C, on a 304 AISI stainless steel, to produce strain induced α′ martensite. Using EBSD analysis and X-ray diffraction methods, the corresponding texture and microstructure evolutions is studied, as well as the γ → α′ transformation mechanism. It is shown that α′ martensite is associated with {1 1 1}_γ faulted bands, partially ε bands, as often reported in the literature for low SFE stainless steels. As a consequence, these deformation bands play a key role in the nucleation and growth of α′ martensite. A micromechanical model is applied to simulate the deformation behavior of the stainless steel as well as the corresponding transformation kinetic and γ texture evolution. Different simulations are proposed, using various assumptions for the γ → α′ transformation mechanism. The simulation data are in better agreement with the experimental ones, when the γ → α′ transformation strain is derived from the Bowles–MacKenzie theory using the (1 1 1)_γ[−1 2 −1]_γ stacking fault shear system as lattice invariant shear.     

Constitutive model of discontinuous plastic flow at cryogenic temperatures

FCC metals and alloys are frequently used in cryogenic applications, nearly down to the temperature of absolute zero, because of their excellent physical and mechanical properties including ductility. Some of these materials, often characterized by the low stacking fault energy (LSFE), undergo at low temperatures three distinct phenomena: dynamic strain ageing (DSA), plastic strain induced transformation from the parent phase (γ) to the secondary phase (α′) and evolution of micro-damage. The constitutive model presented in the paper is focused on the discontinuous plastic flow (serrated yielding) and takes into account the relevant thermodynamic background. The discontinuous plastic flow reflecting the DSA effect is described by the mechanism of local catastrophic failure of Lomer–Cottrell (LC) locks under the stress fields related to the accumulating edge dislocations (below the transition temperature from the screw dislocations to the edge dislocations mode T₁). The failure of LC locks leads to massive motion of released dislocations accompanied by the step-wise increase of the strain rate. The response of stress is defined in terms of four stages within each serration cycle. In the fourth stage, the strain rate sensitivity model with temperature playing the role of relaxation parameter is applied. Identification of parameters of the constitutive model is based on the experimental data collected during a campaign of tensile tests carried out on copper and stainless steel samples immersed in liquid helium (4.5 K), by means of a unique equipment developed at CERN.     

Elasto-visco-plastic modeling of mild steels for sheet forming applications over a large range of strain rates

A physically based elasto-visco-plastic constitutive model is presented and compared to experimental results for three different mild steels. The experiments consist of tensile tests ranging from quasi-static conditions up to strain rates of 10³ s^?1 as well as quasi-static simple and reverse shear tests at different amounts of pre-strain. Additional two-step sequential mechanical tests (Bauschinger and orthogonal effects) have been performed to further evaluate the ability of the model to describe strain-path changes at moderate/large strains. The model requires significantly fewer material parameters compared to other visco-plasticity models from the literature, while being able to describe some of the main features of the strain-rate sensitivity of mild steels. Accordingly, the parameter identification is simple and intuitive, requiring a relatively small set of experiments. The strain-rate sensitivity modeling is not restricted to a particular hardening law and thus provides a general framework in which advanced hardening equations can be adopted.     

Nanocharacterization of creep behavior of multiwall carbon nanotubes/epoxy nanocomposite

High temperature instrumented indentation testing was used to evaluate the mechanical properties of multiwall carbon nanotubes/epoxy nanocomposite system. Reference neat epoxy samples were also tested and compared with the results obtained for the nanocomposite. The nanoindentation creep tests were utilized to provide the creep strain rate sensitivity parameter, the contact creep compliance and the time-dependent deformation under constant loads. Different thermo-mechanical conditions comprising three temperatures of 25, 40 and 55 °C and three loads of 1, 2 and 3 mN were utilized. The improvements in the properties were not as high as anticipated through the use of mixture rule, indicating insufficient dispersion. However, variations in modulus, hardness and creep strain rate sensitivity parameter obtained using nanoindentation showed quantifiable differences between the MWCNTs nanocomposite and epoxy specimens.The comparison of the creep strain rate sensitivity A/d(0) from short term, 60 s, creep tests and the creep compliance J(t) from the long term, 1800 s, creep tests suggests that former parameter is a more useful comparative creep parameter than the creep compliance. The analysis of the creep strain rate sensitivity clearly revealed that the addition of MWCNTs to a commercial epoxy reduced the creep rate. This reduction of creep rate sensitivity parameter was observed particularly at thermal environments just below the glass transition temperature.     

Characterization of the post-necking strain hardening behavior using the virtual fields method

The present study aims at characterizing the post-necking strain hardening behavior of three sheet metals having different hardening behavior. Standard tensile tests were performed on sheet metal specimens up to fracture and heterogeneous logarithmic strain fields were obtained from a digital image correlation technique. Then, an appropriate elasto-plastic constitutive model was chosen. Von Mises yield criterion under plane stress and isotropic hardening law were considered to retrieve the relationship between stress and strain. The virtual fields method (VFM) was adopted as an inverse method to determine the constitutive parameters by calculating the stress fields from the heterogeneous strain fields. The results show that the choice of a hardening law which can describe the hardening behavior accurately is important to derive the true stress–strain curve. Finally, post-necking hardening behavior was successfully characterized up to the initial stage of localized necking using the VFM with Swift and modified Voce laws.     

Anisotropic responses, constitutive modeling and the effects of strain-rate and temperature on the formability of an aluminum alloy

Finite deformation anisotropic responses of AA5182-O, over a wide range of strain-rates (10⁻⁴ to 10⁰ s⁻¹) and temperatures (293-473 K) are presented. The plastic anisotropy parameters were experimentally determined from tensile experiments using specimens from sheet material. Using the experimental results under plane stress conditions, the anisotropy coefficients for Barlat’s yield function (YLD96) were calculated at different strain-rates and temperatures. The correlations obtained from YLD96 are in good agreement with the observed experimental results. The strain-rate sensitivity of AA5182-O alloy changed from negative at 293 K to positive at 473 K. Khan-Huang-Liang (KHL) constitutive model is shown to correlate the observed strain-rate and temperature dependent responses reasonably well. The material parameters were obtained from the experimental responses along the rolling direction (RD) of the sheet. Marciniak and Kuckzinsky (M-K) theory was used to obtain the theoretical strain and stress-based forming limit curves (FLCs) at different strain-rates and temperatures. The experimental result from the published literature is compared with the FLCs from the current study.     

Experimental investigation on martensitic transformation and fracture morphologies of austenitic stainless steel

Formation and nucleation mechanisms (i.e. γ → ε, γ → α′, γ → deformation twins → ε → α′ and γ → ε → α′) of deformation- induced martensite (DIM) have been studied through analytical transmission electron microscopy (TEM) after tensile deformation of AISI 304LN stainless steel at various strain rates (SR) at room temperature (RT). Quantitative metallography has been employed extensively to assess martensitic transformation (MT) as function of strain and SR. It has been observed that the enhancement of SR during tensile deformation promotes the early formation of DIM, while suppressing its saturation value at fracture. Fracture surface morphologies and dimple geometries (i.e. dimple density, dimple diameter and dimple size distribution) have been quantified through image processing (IP) of tensile fractographs. It is noted that at lower SR, dimple density is high while dimple diameter is smaller, and vice versa. Concomitantly, the strength is noted to be low and ductility is high at lower SR, and vice versa. DIM has been found to be responsible for high dimple density at low SR. At high SR, MT is suppressed and hence low dimple density. The variation in SR dependent MT accounts for the variation in dimple metrics vis-à-vis tensile properties.     

Crystal plasticity-based forming limit prediction for non-cubic metals: Application to Mg alloy AZ31B

A viscoplastic crystal plasticity model is incorporated within the Marciniak–Kuczynski (M–K) approach for forming limit curve prediction. The approach allows for the incorporation of crystallographic texture-induced anisotropy and the evolution of the same. The effects of mechanical twinning on the plastic response and texture evolution are also incorporated. Grain-level constitutive parameters describing the temperature dependent behavior of hexagonal close packed Mg alloy, AZ31B, sheets at discrete temperatures are used as a first application of the model. A trade-off between significant strain hardening behavior at lower temperatures (∼150 °C), and significant strain rate hardening at higher temperatures (∼200 °C) lead to similarities in the predicted forming limits. The actual formability of this alloy depends strongly on temperature within this range, and this distinction with the current modeling is related to more localized instability-based failure mechanisms at the lower temperatures than is assumed in the M–K approach. It is shown that the strain path dependence in the strain hardening response is significant and that it influences the forming limits in a predictable way. For broader applicability, a means of incorporating dynamic recrystallization into the crystal plasticity model is required.     

Cyclic behavior of extruded magnesium: Experimental, microstructural and numerical approach

The present study aims at determining the influence of cyclic straining on the behavior of pure extruded magnesium. For this purpose, tensile, compressive and cyclic tests are performed (small plastic strains are applied (Δε^p/2 = 0.1% and 0.4%). Deformation mechanisms (slip and twin systems) have been observed by TEM and the different critical resolved shear stress (CRSS) have been determined. Based on microscopic observations, a crystal-plasticity-based constitutive model has been developed. The asymmetry between tensile and compressive loadings mainly results from the activation of hard slip systems in tension (such as 〈a〉 pyramidal and prismatic and 〈c + a〉 pyramidal glides) and twinning in compression. It is shown that basal slip is very easy to activate even for small Schmid factors. Numerical simulations reveal that untwinning in tension subsequent to compression must be considered to correctly fit the experimental S-shaped hysteresis curves. TEM observations indicate also intense secondary slips or twins inside the mother twins under cyclic conditions, so that twinning in compression and dislocation glide in tension are affected by cycling. The polycrystalline model allows to predict slip activities and twin volume fraction evolutions.     

A new unified constitutive model with short- and long-range back stress for lead-free solders of Sn–3Ag–0.5Cu and Sn–0.7Cu

A series of tensile tests of Sn–3Ag–0.5Cu and Sn–0.7Cu lead-free solders were investigated at various strain rates from 1 × 10⁻⁴ s⁻¹ to 1 × 10⁻² s⁻¹ and over a wide temperature range from 25 ^oC to 150 ^oC. Two-step strain rate jump tests, three-step short term creep tests with stress jump, and uniaxial ratcheting tests were also conducted. Based on the test data, a new constitutive model was proposed with a simple formulation and only eight material constants which can be easily obtained. The model employs two carefully defined back stress components to simulate the loading/unloading asymmetry phenomenon in uniaxial ratcheting tests. Different evolution rules of short-range back stress were given for loading and unloading stage, which provides the model ability to simulate the asymmetry in hysteresis loops. The proposed model presents good simulation of uniaxial tensile tests, strain rate jump tests, short term creep tests with stress jump, and uniaxial ratcheting tests.     

High temperature strength and failure of the Ni-base superalloy PM 3030

The strength, fatigue life and fracture behavior of the oxide dispersion strengthened (ODS) nickel-base superalloy PM 3030 are investigated. The high Al content in PM 3030 leads to the formation of coherent γ′ particles and, thus, to additional precipitation strengthening. A coarse and elongated grain structure (R34) and two isotropic batches with mean grain sizes of 1 μm (R90) and 17 μm (R901315) are considered. Compressive constant strain rate tests and high cycle fatigue (HCF) tests are performed. Optical, scanning and transmission electron microscopy (OM, SEM and TEM) are carried out. The properties are compared with those of the solely oxide dispersion strengthened Ni-base alloy PM 1000 [Estrin, Y., Heilmaier, M., Drew, G., 1999. Creep properties of an oxide dispersion strengthened nickel-base alloy: the effect of grain orientation and grain aspect ratio. Mater. Sci. Eng. A 272(1), 163–173]. It is found that additional γ′ hardening provides an increase in quasi-static strength by about a factor 2 and in HCF life by about a factor 10²–10³ at temperatures up to 850 °C. When fatigue life is compared at a fixed ratio of stress amplitude-to-yield or ultimate compressive strength, R34 shows a fatigue life similar to that of PM 1000 at lower temperature (e.g. 600 °C) indicating that the quasi-static strength advantage is proportionally translated into improved fatigue performance; for higher temperatures (850 °C) however, R34 shows a shorter fatigue life as compared to PM 1000. Grain size reduction, as exemplified with the fine grain R90 batch, also provides an increase in strength up to the equicohesion temperature (T_E) [Dieter, G.E., 1986. Mechanical Metallurgy. SI Metric ed. McGraw-Hill Book Company, London]. Above T_E, faster diffusion and grain boundary sliding [Raj, R., Ashby, M.F., 1971. On the grain boundary sliding and diffusional creep. Metall. Trans. 2, 1113–1127; Spingarn, J.R., Nix, W.D., 1978. Diffusional creep and diffusionally accommodated grain rearrangement. Acta Metall. 26, 1389–1398] lead to a drastic drop in strength for the R90 material. In contrast, the batch with intermediate grain size (R901315) shows strength comparable to that of R34 up to 850 °C. Furthermore, R901315 shows improved crack tolerance compared to its coarse grain counterpart R34. Due to premature crack initiating coarse oxide particles however, R901315 does not show any improvement in elongation to failure during tensile tests. Eliminating those coarse particles is expected to improve the ductility and toughness of this isotropic batch.     

DP钢板应变路径多步演变下的弹塑性力学行为

针对DP高强双相钢板在复杂载荷作用下的弹塑性力学特征,提出利用三步拉伸力学实验,对比分析单轴循环加载和非等轴加载下材料的各向异性硬化、永久软化和弹性模量衰减特性等力学行为,揭示应变路径多步演变下的弹塑性力学特性.研究结果表明:材料再加载初期的瞬态行为与应变路径有关,在初期瞬态阶段显示出明显的各向异性,且再加载角度、预应...     

Plastic anisotropy and the role of non-basal slip in magnesium alloy AZ31B

Mechanistic explanations for the plastic behavior of a wrought magnesium alloy are developed using a combination of experimental and simulation techniques. Parameters affecting the practical sheet formability, such as strain hardening rate, strain rate sensitivity, the degree of anisotropy, and the stresses and strains at fracture, are examined systematically by conducting tensile tests of variously oriented samples at a range of temperatures (room temperature to 250 °C) and strain rates (10⁻⁵–0.1 s⁻¹). Polycrystal plasticity simulations are used to model the observed anisotropy and texture evolution. Strong in-plane anisotropy observed at low temperatures is attributed to the initial texture and the greater than anticipated non-basal cross-slip of dislocations with 〈a〉 type Burgers vectors. The agreement between the measured and simulated anisotropy and texture is further validated by direct observations of the dislocation microstructures using transmission electron microscopy. The increase in the ductility with temperature is accompanied by a decrease in the flow stress, an increase in the strain rate sensitivity, and a decrease in the normal anisotropy. Polycrystal simulations indicate that an increased activity of non-basal, 〈c + a〉, dislocations provides a self-consistent explanation for the observed changes in the anisotropy with increasing temperature.     

Forming of aluminum alloys at elevated temperatures – Part 1: Material characterization

A temperature-dependent anisotropic material model for use in a coupled thermo-mechanical finite element analysis of the forming of aluminum sheets was developed. The anisotropic properties of the aluminum alloy sheet AA3003-H111 were characterized for a range of temperatures 25–260 °C (77–500 °F) and for different strain rates. Material hardening parameters (flow rule) and plastic anisotropy parameters (R₀, R₄₅ and R₉₀) were calculated using standard ASTM uniaxial tensile tests. From this experimental data, the anisotropy coefficients for the Barlat YLD96 yield function [Barlat, F., Maeda, Y., Chung, K., Yanagawa, M., Brem, J.C., Hayashida, Y., Lege, D.J., Matsui, K., Murtha, S.J., Hattori, S., Becker, R.C., Makosey, S., 1997a. Yield function development for aluminum alloy sheets. J. Mech. Phys. Solids 45 (11/12), 1727–1763] in the plane stress condition were calculated for several elevated temperatures. Curve fitting was used to calculate the anisotropy coefficients of Barlat’s YLD96 model and the hardening parameters as a function of temperature. An analytical study of the accuracy and usability of this curve fitting technique is presented through the calculation of plastic anisotropy R-parameters and yield function plots at different temperatures.     

Non-coaxiality of strain increment and stress directions in cross-anisotropic sand

An experimental program was carried out in a recently developed torsion shear apparatus to study the non-coaxiality of strain increment and stress directions in cross-anisotropic deposits of Fine Nevada sand. Forty-four drained torsion shear tests were performed at constant mean confining stress, σ_m, constant intermediate principal stress ratios, as indicated by b = (σ₂ − σ₃)/(σ₁ − σ₃), and constant principal stress directions, α. The experiments were performed on large hollow cylinder specimens deposited by dry pluviation and tested in an automated torsion shear apparatus. The specimens had height of 40 cm, and average diameter of 20 cm, and wall thickness of 2 cm. The stress–strain behavior of Fine Nevada sand is presented for discrete combinations of constant principal stress direction, α, and intermediate principal stress. The effects of these two variables on the non-coaxiality are presented. The experiments show that the directions of the strain increments do not in general coincide with the directions of stresses, and there is a switch from one to the other side between the two quantities.     

Yield criterion and elasto-plastic damage constitutive model for frozen sandy soil

A series of triaxial compression tests was carried out on a frozen sandy soil under confining pressures of 0–18 MPa at −6 °C. The experimental results indicate that, the strength of frozen sandy soil increases versus the increase in the confining pressures when σ₃ ? 3 MPa, but decreases when σ₃ > 3 MPa. This phenomenon is called the strengthening and weakening effects of confining pressures. A yield function, considering both effects, is proposed using the experimental method according to Drucker’s postulate, and the mathematical expression of the hardening parameter, which can describe the softening and hardening phenomenon, is provided. An elasto-plastic constitutive model for frozen sandy soil is developed. Based on the continuum damage theory, the cross anisotropic damage variables are deduced and their change regularities are investigated. Then the elasto-plastic damage constitutive model is proposed by introducing damage variables into elasto-plastic constitutive model. The validity of the model is verified by comparing its modeling results with experimental results obtained from triaxial tests. It is found that, this model can predict the deformation regularity of frozen soil exactly. It can simulate the stress–strain process under high confining pressures when pressure melting phenomena appear especially well.