Ultrasonic measurement of sheet steel texture and formability: Comparison with neutron diffraction and mechanical measurements

Ultrasonic measurements were made on a set of thin steel sheets, using the lowest-order shear horizontal mode (SH₀-mode) and lowest-order symmetric Lambwave mode (S₀-mode). The velocities of these modes were measured as a function of angle relative to the sheet rolling direction. From the data reduction it is, in theory, possible to (1) partially characterize the texture of the sheet, and (2) predict the plastic strain ratio (r-value). The plate texture can be completely characterized by quantities known as orientation distribution coefficients (ODCs). The lowest-order ODCs can be obtained from our measurements; these were compared with ODCs measured by neutron diffraction, with good agreement for the dominant ODC. The r-value is a commonly used measure of sheet formability. It is typically measured mechanically with uniaxial tension specimens subjected to large plastic strain. Therefore, the r-value test is destructive and time consuming. We found a good correlation between S₀-mode velocity measurements and , the average in-plane r-value. Consequently, the use of noncontacting electromagnetic-acoustic transducers (EMATs) may offer an online nondestructive measurement of sheet formability.Contribution of U.S. Department of Commerce, National Institute of Standards and Technology; not subject to copyright.     

Comparison of simulated and experimental strain ratio R for different grain shapes in sheet metal

Abstract

Predicting mechanical properties by means of a simple indicator is of great importance to sheet metal forming. An important parameter characterising the formability of a rolled sheet is the plastic strain ratio R which is strongly determined by the texture. The angular variation of R value in the rolling plane has been calculated from the orientation distribution function using the Bunge method. The following grain interaction models have been tested: two Taylor full constraint models ({hkl}〈111〉 and {110}〈111〉 plus {112}〈111〉), three relaxed constraints models (RC₄ , RC₃ , RC₂ ), and the Sachs–Kochendörfer model. The shapes of the grains were investigated by means of the secant method which allowed the spatial parameters of the two- dimensional structure image to be measured. The comparison of simulated and experimental data has proved that in the case of aluminium killed steels, the relaxed constraints model RC₄ is the best predictor of the plastic strain ratio. Good results were also obtained using the Sachs-Kochendörfer model.     

Influence of grain size on plastic anisotropy in low-carbon steels

Abstract

The plastic anisotropy of textured polycrystalline materials has often been described by the r-value – the ratio of the width and thickness strains. The measured –-values of low-carbon steels for larger grain sizes are found to agree reasonably well with values calculated by the authors on the basis of the Taylor theory. In steels with small grain sizes the absolute level of r-value is not predicted particularly well, but the variation with testing direction (planar anisotropy) is predicted well. Calculations showed that in all cases the instantaneous anisotropy parameter ρ as a function of strain, when extrapolated to zero strain, agreed with the value predicted from the measured texture. With small grain sizes a sudden drop in ρ was observed with increasing strain, this being complete within 2–3% of strain. The influence of grain size on the plastic anisotropy can be understood if it is assumed that the grain boundary resistance parameter K in the Hall–Petch relation depends on the contraction ratio – in a different way from the Taylor factor M(q). Measurements of the Hall–Petch constant in plane-strain compression support this view.

MST/84     

Effects of crystallographic texture on ultrasonic wave velocities in steels

Abstract

Studies of ultrasonic wave velocities in commercial steel sheet products have been made and the results have been interpreted in terms of crystallographic textures measured by X-ray diffraction. Elasticity tensors were calculated as weighted averages of the Voigt and Reuss bounds using texture coefficients together with single crystal stiffness data, and these were then employed to predict the ultrasonic wave velocities. For guided bulk waves of types S_o and SH_o excellent agreement was obtained between measured and predicted values. The application of these types of measurements to process control in metallurgical annealing lines has been briefly discussed.     

Determination of Sheet Steel Formability Using Wide Band Electromagnetic-Acoustic Transducers

Abstract

An electromagnetic-acoustic transducer (EMAT) system was used in conjunction with a “sampled” CW signal-processing method to generate, receive, and process longitudinal and shear waves in thin steel sheets. Using the system, swept-frequency measurements were made up to 7.5 MHz. To relate the measurements to sheet steel formability, a dimensionless frequency ratio, K, was computed from the resonant frequencies. From theoretical considerations, K should be related to a measure of steel sheet formability, r . This parameter is traditionally measured by plastically deforming uniaxial tension specimens. Good correlation was found between K and r for a set of steel sheet representative of those typically used to produce automobile body parts.     

In-plane anisotropy in low cycle fatigue properties of and bilinearity in Coffin-Manson plots for quaternary AI-Li-Cu-Mg 8090 alloy plate

Abstract

Low cycle fatigue (LCF) behaviour as a function of test direction was studied for a quaternary Al–Li–Cu–Mg alloy. The analysis of the variation in fatigue life with plastic strain amplitude ??_p/2 or with average stress amplitude ?σ/2 or with plastic strain energy per cycle ?W_p, revealed bilinear power law relationships in all the test directions. The transition strain values in the Coffin–Manson plots were seen to match closely with those obtained in the cyclic stress response as well as with the cyclic stress–strain relationships of the alloy. The observed bilinear behaviour in these LCF properties was attributable to a change in deformation as well as to the deformation assisted fracture mode. The alloy revealed significant in plane anisotropy in the LCF properties. The observed anisotropy was found to result from the combined effects of strong crystallographic texture and grain fibering.

MST/3016     

Crystallography-based prediction of plastic anisotropy of polycrystalline materials

The on-line prediction of metal sheet formability requires that both material characterization (texture identification) and yield loci predetermination be done in very shor time intervals. Of two applicable approaches, i.e., continuum mechanics and crystallography-based methods, only the latter are suitable for this purpose. Several models of plasticity of a polycrystalline material were reviewed, and their applicability to the prediction of plastic anisotropy of face-centered cubic (FCC) metals was evaluated. A tailored set of cold-rolled copper alloy samples was designed and manufactured, representing the wide spectrum of textures and cold work levels typical for the sheet metal industry. The texture was quantitatively described in the form of the orientation distribution functions derived by the inversion of four incomplete pole figures. The Taylor-Bishop-Hill model was applied in order to calculate the planar variation of the plastic strain ratio. The continuum mechanics of textured polycrystals approach was also used for the prediction of the plastic strain-rate ratio for the same set of deformed materials. The theoretical predictions were compared with the plastic strain ratios measured in tensile tests using strain gauges. The applicability of the models for prediction of the plastic anisotropy of FCC metals was discussed in view of the operating deformation mechanisms and other factors such as strain hardening sensitivity and grain size/shape effects.     

On the formability of sheet steels

Formability of sheet steel in stamping operation primarily depends on strain hardening exponent (n), average plastic strain ratio ( ) and the maximum strain the material can undergo before the onset of localized necking. The formability parameters (n and ) and the forming limit diagrams have been evaluated for a variety of sheet steel products, extensively used for press forming of components of diverse shapes e.g. extra deep drawing quality auto-body sheets, high strength cold rolled sheets, LPG steel for gas cylinders, austenitic and ferritic stainless steels, etc. The effect of sulphide shape control on formability of hot rolled HSLA steel has also been studied. Additionally, the press performance of auto-body sheets and austenitic stainless steels have been monitored and evaluated at customer’s end for complete information on the formability.     

Formability of two aluminium alloys

Abstract

The suitability of two recently developed aluminium alloys (an Al–Mg–Mn alloy and an Al–Li–Cu alloy) for press forming applications has been examined. The characterisation involved the experimental determination of microstructural aspects, tensile properties, and formability parameters such as average plastic strain ratio and planar anisotropy. The forming limit diagram has been experimentally evaluated. A detailed analysis of the strain distribution profiles obtained from punch stretching experiments has been attempted. An attempt has been made to correlate the crystallographic texture with the formability parameters. The fracture surfaces of the punch stretched samples were observed using scanning electron microscopy with a view to obtaining a correlation between fracture behaviour and formability. The alloys, in particular the Al–Mg–Mn alloy, have been found to possess good stretchability but both show very limited drawability. Texture analysis indicated negligible earing during deep drawing. These alloys are suitable for stamping applications where stretching constitutes the major proportion of the deformation.     

Lamb waves for non-contact fatigue state evaluation of composites under various mechanical loading conditions

Methodologies for non-destructive evaluation of mechanically induced fatigue in fibre reinforced polymers are discussed. Specimens made of non-crimp glass fabric are fatigued using three different load ratios (tension–tension, tension–compression, and compression–compression). The investigation involves two loading directions (0° and 90°) of the quasi–orthotropic composite. Based on mode conversion of air-coupled ultrasound to Lamb waves, variation in a₀-mode velocity is measured in a non-contact and single-sided access configuration. The velocity measurements are performed within and outside the servo-hydraulic test rig used for inducing fatigue damage. Formation of cracks monitored in the transparent composite results in degradation of stiffness observed by the test rig. Decrease in a₀-mode velocity caused by fatigue is shown to correlate closely with stiffness degradation for all loading ratios and directions. The correlation is studied by calculating a₀-mode velocities from single-ply properties whose stiffness degradation was determined using the observed crack densities and a finite element based model.     

Influence of out-of-plane compression stress on limit strains in sheet metals

The prediction of the forming limits of sheet metals typically assumes plane stress conditions that are really only valid for open die stamping or processes with negligible out-of-plane stresses. In fact, many industrial sheet metal forming processes lead to significant compressive stresses at the sheet surface, and therefore the effects of the through-thickness stress on the formability of sheet metals cannot be ignored. Moreover, predictions of forming limit curves (FLC) that assume plane stress conditions may not be valid when the forming process involves non-negligible out-of-plane stresses. For this reason a new model was developed to predict FLC for general, three-dimensional stress states. Marciniak and Kuczynski (Int J Mech Sci 9:609-620, 1967) first proposed an analytical method to predict the FLC in 1967, known as the MK method, and this approach has been used for decades to accurately predict FLC for plane stress sheet forming applications. In this work, the conventional MK analysis was extended to include the through-thickness principal stress component (σ ₃), and its effect on the formability of different grades of sheet metal was investigated in terms of the ratio of the third to the first principal stress components (). The FLC was predicted for plane stress conditions (β = 0) as well as cases with different compressive through-thickness stress values (β ≠ 0) in order to study the influence of β on the FLC in three-dimensional stress conditions. An analysis was also carried out to determine how the sensitivity of the FLC prediction to the through-thickness stress component changes with variations in the strain hardening coefficient, in the strain rate sensitivity, in plastic anisotropy, in grain size and in sheet thickness. It was found that the out-of-plane stress always has an effect on the position of the FLC in principal strain space. However, the analysis also showed that among the factors considered in this paper, the strain hardening coefficient has the most significant effect on the dependency of FLC to the through-thickness stress, while the strain rate sensitivity coefficient has the least influence on this sensitivity.     

Application of nondestructive techniques for the prediction of elastic anistropy of a textured polycrystalline material

Effect of processing parameters including cold work and grain size on texture development in copper and 68:32 -brass thin sheets is investigated. The preferred orientation of grains (texture) is represented quantitatively by the orientation distribution function (ODF) as derived either by X-ray diffraction or by ultrasonic velocity measurements. The texture-induced elastic moduli are derived in the sheet plane at various orientations to the rolling direction. The predicted values of elastic moduli are compared with the mechanically measured ones. An attempt is made to empirically correlate ODF coefficients to the mechanically measured elastic modulus and plastic strain ratio (r-value). The sources of discrepancies such as the limitations of the measuring techniques and the models applied are discussed.     

Microstructure and texture evolution during incremental sheet forming of AA1050 alloy

In incremental sheet forming higher limiting strain can be achieved compared to the conventional sheet metal forming process, which results in increased formability. The higher level of strain may be accompanied by non-uniform thinning. Thus, the different sections in a component may undergo different levels of deformation. In the present work a truncated cone of AA1050 H14 alloy was formed using the incremental sheetmetal forming (ISF) technique. The deformation mechanism during ISF was studied by investigating the microstructural and texture evolution in the truncated cone along the thickness of the cone wall. High resolution electron backscatter diffraction was performed at different sections of the formed truncated cone. The results show the formation of subgrains in different sections of the cone. At higher strains, grains become thin and elongated which results in grain fragmentation and formation of small grains. These small grains undergo complete recovery process and new grain boundaries (low and high angle) are formed within the thin elongated grains. Further, the evolution of shear texture shows the evidence of shear mode of deformation during incremental sheet forming. Thus, the presence of through thickness shear could be used for understanding the higher forming limit in the ISF process.

     

Effect of carbon concentration on tensile behaviour of pearlitic steels

Abstract

A quantitative relationship between flow stress and microstructure is studied for pearlitic steels incorporating 0.39 - 0.77 wt-% carbon. The distribution of true lamellar spacing (S ₀) is determined. It is found that S ₀ depends on carbon concentration and pearlite transformation temperature accompanying a considerable distribution. The 0.2% proof stress is described as a function of the averaged S ₀ but the influence of the accuracy in S ₀ measurement precludes satisfactory prediction of the 0.2% proof stress. High work hardening corresponds to the generation of phase stress caused by misfit plastic strain between ferrite and cementite. The stress partitioning behaviour between ferrite and cementite is verified by in situ neutron diffraction during tensile deformation.     

Structure,anisotropy, and properties of hot rolled AA 5083 alloy

Abstract

The changes in structure and substructure occurring during homogenisation and hot rolling of an Al–5Mg alloy (AA 5083) have been investigated. It is shown that a homogenisation treatment is beneficial and that the resulting structure can be related to processing parameters. The results suggest that the substructure morphology is dependent upon the total strain, but this has not been quantified. The development of texture was also studied and it is shown to be almost invariant with temperature, but strongly strain dependent. The anisotropy so produced yielded plastic strain ratios that were found to be strongly dependent upon the rotated copper texture intensity. The deep drawing behaviour of the hot rolled sheet was investigated by employing cupping tests and it is shown that a relationship exists between the earing value and the subgrain size.

MST/I086     

Measurement of texture and formability parameters with a fully automated,ultrasonic instrument

A fully automatic, ultrasonic instrument to measure texture and formability parameters on metal sheet is described. Arrays of EMAT transducers are used to transmit and receiveS _o Lamb waves propagating at 0°, 45°, and 90° with respect to the rolling direction. By analyzing the frequency dependence of the phase of the received signals, the long wavelength limit of the velocities is obtained. Included is a discussion of this algorithm, and subsequent processing steps to predict the ODC'sW ₄₀₀,W ₄₂₀, andW ₄₄₀. On steel, the prediction of drawability parametersr and r based on a correlation developed previously by Mould and Johnson is also discussed. Results of blind field trials at facilities of three suppliers/users of steel sheet for automotive applications and one supplier of aluminum sheet for beverage can production are reported. The former confirmed the Mould-Johnson correlation for lowr material but indicated that refinements are needed for modern steels with highr. The aluminum data suggest a correlation between W₄₄₀ and the degree of four-fold earing.     

Improvement in formability of aluminum alloy sheet by enhancing geometrical hardening

Individual grains in a polycrystal rotate during plastic deformation. This leads to a change in the crystallographic texture, and results in an increase or decrease of the macroscopic flow stress of the material. Such a change of strength as a result of grain rotations is called geometrical or texture hardening/softening. In the present study, for textured aluminum alloy sheets, the geometrical hardening/softening effect in the in-plane plane-strain stretching mode is numerically investigated using a generalized Taylor-type polycrystalline model. It is found that the cube texture () exhibits significant geometrical hardening when the major stretching direction is inclined at 45° relative to the orthotropic axes, and that a cube texture rotated about the normal direction (ND) shows a notable degree of geometrical hardening for any in-plane orientation of the sheet. Using the Marciniak-Kuczyński-type approach, forming limits for these textured sheets are analyzed. It is found that geometrical hardening definitely enhances the formability. It is, therefore, strongly suggested that texture control guided by the present results may be highly effective in producing aluminum alloy sheets with higher formability.     

Tensile property and cold formability of a Mg96Zn2Y2 alloy sheet with a long-period ordered phase

The tensile property and cold formability of a Mg₉₆Zn₂Y₂ alloy sheet containing Mg-, long-period ordered (LPO)-, and Mg₃Zn₃Y₂-phases were investigated. The Mg₉₆Zn₂Y₂ alloy sheet exhibited a high yield stress of 320 MPa and elongations of 11% at room temperature and could be prepared by hot-rolling. After, annealing at 773 K for 0.6 ks, although the yield stress decreased to 200 MPa, elongation increased to 20%. Texture randomization due to re-crystallization of the Mg phase that occurred in the annealed Mg₉₆Zn₂Y₂ alloy sheet was confirmed by EBSD analysis. The formability of a Mg₉₆Zn₂Y₂ alloy sheet and an AZ31-O sheet was evaluated via a 90° V-bending test at room temperature. The annealed Mg₉₆Zn₂Y₂ alloy sheet could be bent without cracking with a minimum bending radius per thickness of R/t = 3.3, which is less than that of the as-rolled Mg₉₆Zn₂Y₂ alloy sheet and the AZ31-O sheet. This improvement in the cold formability of the Mg₉₆Zn₂Y₂ alloy sheet is considered due to an increase in randomness of the Mg phase that results from re-crystallization of the Mg phase.     

Low cycle fatigue resistance of Al–Li alloys

Abstract

Low cycle fatigue (LCF) resistance data from binary Al–Li, ternary Al–Li–Cu, and quaternary Al–Li–Cu–Mg alloys have been compiled and discussed. The LCF resistance is measured in terms of the variation of the number of reversals to failure 2N _fwith the plastic strain amplitude Δ? _p /2 as well as a modified average plastic strain energy per cycle (ΔW _p )_modified , obtained at different applied total strain amplitudes (Δ? _t /2). The data show the effects of microstructural features, namely dominant strengthening precipitates and the degree of recrystallisation as well as crystallographic texture. Lithium content, when in excess of 2·5 wt-%in aluminium decreases the low cycle fatigue resistance the most. The degree of aging, the degree of recrystallisation, and the degree of texture also influence the LCF resistance; among which the effect of the degree of aging is the most pronounced. The effects of lithium content in aluminium solid solution and strengthening precipitates obtainable by the change in the Li/Cu ratio are found to be marginal. Based on a modified total cyclic plastic strain energy till fracture, it is shown that most of the Al–Li alloys exhibit degradation in their LCF resistance in both hypotransition (higher fatigue lives) and hypertransition (lower fatigue lives) regions. Such degradation is attributed to the combined effects of mechanical fatigue, strain localisation through dislocation–precipitate interaction, environmental effects, and finally strain localisation through the high angle grain boundaries. In comparison with the currently used 2XXX and 7XXX series aluminium alloys, Al–Li alloys require substantial improvement before they can be considered for fatigue critical applications.     

Microstructure and mechanical behaviour of asymmetric extruded Mg–3Al–1Zn alloy sheets

Abstract

Microstructural evolution and mechanical responses of Mg–3Al–1Zn (AZ31) sheet processed by the asymmetric extrusion (ASE) and conventional extrusion (CE) are examined. Mechanical properties of ASE sheets were remarkably enhanced compared with CE samples. This is attributed to the subdivision of the asymmetric extrusion die along the flow passage equipped with a chamfer on one side, which would trigger the angular spread of the basal texture by introducing an asymmetry shear deformation. Moreover, subsequent annealed ASE specimens show a significant weakening of the basal texture and a combination of the superior stretch formability.