Cold deformation behavior of graphitized carbon steel

The cold compression test of a strain rate 1s-1 for graphitized carbon steel containing C of 0. 43 mass% with ferrite and graphite was carried out using Gleeble- 3500 thermal simulation machine, the characteristics of the stress- strain relationship was analyzed, and metallographic analysis in the large deformation zone of the compressed samples with different reduction was investigated by optical microscope, field emission scanning electron microscopy and micro hardness tester. The results show that there exists peak stress on the stress- strain curve, namely, 645MPa, the corresponding peak strain is 0. 43; in process of the compressive deformation, morphologies of ferrite and graphite in the large deformation zone on the longitudinal section of the compressed samples gradually become fibrous with increasing the reduction; thereinto, the deformation of graphite particles is realized by means of sliding deformation between basic planes of graphite, shear deformation between substructures of graphite particles, as well as elongation of compacted section near the base of the ferrite of the deformed graphite particles; microhardness of ferrite increases with increasing the reduction, it indicate that ferrite is in a state of hardening, but, increase amplitude of microhardness in the process of compressive deformation after peak stress is decreased. Therefore, based on increase amplitude of microhardness of ferrite and microstructure of the deformed graphite particles, it can be concluded that in process of the compressive deformation after peak stress, deformation of graphite particles in the large deformation zone plays a major role, a deformation of ferrite plays a secondary role (it is mainly to coordinate the deformation of graphite particles), this is one of the main reason that stress decreases in the compressive deformation after peak stress.     

Modeling the Flow Curve Characteristics of 410 Martensitic Stainless Steel Under Hot Working Condition

The hot deformation behavior of AISI 410 martensitic stainless steel was investigated by conducting hot compression tests between 1173 K (900 °C) and 1423 K (1150 °C) and between strain rates of 0.001 s⁻¹ to 1 s⁻¹. The hyperbolic sine function described the relation well between flow stress at a given strain and the Zener–Hollomon parameter (Z). The variation of flow stress with deformation temperature gave the average value of apparent activation energy as 448 kJ/mol. The strain and stress corresponding to two important points associated with flow curve (i.e., peak strain and the onset of steady-state flow) were related to the Z parameter using power-law equations. A model also was proposed based on the Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation to estimate the fractional softening of dynamic recrystallization at any given strain. This model can be used readily for the prediction of flow stress. The values of n and k, material constants in the JMAK equation, were determined for the studied material. The strains regarding the peak and the onset of steady-state flow were formulated in term of applied strain rate and the constants of the JMAK equation. A good agreement was found between the predicted strains and those obtained by the experimental work.     

X-ray determination of stress-strain distribution in unnotched C-rings: A link from micro- to macromechanics

An alloy 600 C-ring was subjected to various strain levels and the deformation process was monitored by a computer-aided rocking curve analysis (CARCA) of individual grains. Calibration curves were established, relating the average rocking curve halfwidth of the sampled grain population to the prevailing stress and strain. The strain analysis was carried out as a function of the angular position along the periphery of the C-ring for surface layers and layers at different depth distances. Up to C-ring closure at the nominal strain at 3.3%, the induced plastic strains were confined to a surface layer of 30–40 μm in depth. The large strains and strain gradients below the surface were induced in the apex and near apex region. The extent and spread of microdeformation inhomogeneity increased with increased applied strain. At ring closure, some grains exhibited very large plastic strain while others were not affected by the deformation process. No agreement was obtained on the angular strain dependence between experimental observations and theoretical calculations, if upon straining the induced shape changes were not taken into account. Good agreement on the angular strain dependence for the apex and near apex region was achieved between experiment and theory, when shape changes were taken into account by partitioning the C-ring periphery into sectors with varying radii and inserting the experimentally determined values into the calculations. It was concluded that the CARCA X-ray method can be a very useful research tool in aiding and guiding mathematical modeling of nonlinear inelastic behavior of solids by disclosing important microstructural and micromechanical aspects.     

Limit-State Curve of Base-Course Material and Its Relevance for Resilient Modulus Testing

The limit state characteristics of base-course granular materials were obtained using a typical triaxial testing equipment devoted to the measurement of resilient modulus. Accurate monitoring of axial strain during isotropic and anisotropic compression was used to determine the stress conditions where significant irrecoverable strains occur for samples prepared by static compression, Proctor rammer, and vibratory compaction. The limit state curve is highly anisotropic, centered about the q/p = 1 line. It is sensitive to sample preparation technique and fines content. The Strategic Highway Research Program (SHRP) procedure corresponds to stress paths during conditioning and repeated loading that remain within the limit state curve of the control base course material containing 3.5% fines. The resilient modulus values reflect henceforth the behaviour of the same material with its original particle contact distribution. The Laboratoires des Ponts et Chaussées (LCPC) procedure is characterized by stress paths that cross the original limit state curve of the Proctor compacted samples. Particle contact distribution changes thus continuously as the limit state curve expands in response to the various stress paths used in this procedure. The resilient modulus values correspond to samples with different fabrics. A simple procedure based on isotropic loading has been proposed for the determination of a simplified limit state curve of base course materials with the intent of specifying the testing conditions for obtaining adequate resilient modulus values.     

Experimental Methodology for Obtaining the Flow Curve of Sheet Materials in a Wide Range of Strains

An experimental approach for determining the stress–strain curve over a large range of strains through tensile test is introduced. The novel aspect of the proposed approach is to apply different degrees of cold working on the sheet metal specimens before tensile test. By adding the pre‐strain derived from cold working to the strain from tensile test, the corresponding stress–strain curves can be shifted to large strains. Since the variation trend of these curves is in high coincidence with the results from compression test, it is convinced that the stress–strain curve of tensile test over a large range of strains can be experimentally extrapolated based on such an approach, especially aiming at medium‐thick sheet metal. Based on the tensile test results, five different extrapolation models were evaluated with respect to different sampling dataset. It was revealed that the true stress–plastic strain curve over a given strain range could be approximated well by the extrapolation models of Ludwik, Ghosh, and Hocket‐Sherby based on sampling data points of standard tensile test combined with a prescribed data point from tensile test after cold working.     

On the measurements of superplasticity in an Al-Cu alloy

The usual method of measuring the strain rate sensitive ‘m’ values of superplastic materials through differential cross-head speed is found to result in improperly definedm values;m is found to depend strongly on the strain to which the material is subjected, especially at low strains. In this connection, the shape of the log stress-log strain rate curve is examined for the Al-33 wt pct Cu eutectic alloy. The inherent grain growth of the very fine grains which occurs during deformation, and the strain dependence ofm at low strains, are shown to be the causes of the familiarS shape of the log stress-log strain rate curves for the Al-Cu alloy. At high strains (15 to 20 pct and higher) where the stress is no longer importantly strain sensitive, the log stress-log strain rate curve is a straight line of slope near 0.5. The elongation at fracture also does not go through a maximum but continues to increase slowly to the lowest strain rate examined: 10^-7 per s.     

Grain-size strengthening in terms of dislocation density measured by resistivity

The effect of grain size on flow stress has been investigated in terms of dislocation density. The measurement of dislocation density was made for nickel having a high stacking fault energy, by means of electrical resistivity with which the dislocation density can be measured up to larger strains compared with transmission electron microscopy. It was found that the dislocation density for a given strain in specimens deformed in tension at 77 and 295 K increases in a linear manner with the reciprocal of grain size. It was also ascertained that the flow stress is proportional to the square root of dislocation density, irrespective of grain size, deformation temperature and the amount of plastic strain (ϵ). From the above two relationships, an equation between flow stress and grain size was obtained in a general form, which gives the Hall-Petch relation as the limited case at yield point or at small strains.     

On the measurements of superplasticity in an Al-Cu alloy

The usual method of measuring the strain rate sensitive ‘m’ values of superplastic materials through differential cross-head speed is found to result in improperly definedm values;m is found to depend strongly on the strain to which the material is subjected, especially at low strains. In this connection, the shape of the log stress-log strain rate curve is examined for the Al-33 wt pct Cu eutectic alloy. The inherent grain growth of the very fine grains which occurs during deformation, and the strain dependence ofm at low strains, are shown to be the causes of the familiarS shape of the log stress-log strain rate curves for the Al-Cu alloy. At high strains (15 to 20 pct and higher) where the stress is no longer importantly strain sensitive, the log stress-log strain rate curve is a straight line of slope near 0.5. The elongation at fracture also does not go through a maximum but continues to increase slowly to the lowest strain rate examined: 10^-7 per s. Formerly Research Assistant, Department of Metallurgy and Materials Science, MIT.     

A Physical Analysis of the Stress Relaxation Kinetics of Deformed Austenite in C‐Mn Steel

The softening kinetics following hot deformation of austenite have been characterised using the stress relaxation technique. Samples were deformed in compression for a variety of temperatures, strains and strain rates. At low strains where recovery was the only softening mechanism, the stress relaxation kinetics have been analysed using a recovery model previously proposed in the literature, the main parameters being activation energy and activation volume. The activation energy for recovery was found to be 314 kJ/mol, whilst the activation volume was inversely proportional to the internal stress. At higher strains where austenite recrystallization occurred as well, the stress relaxation kinetics were modelled using the recovery model combined with a single grain model for recrystallization. Reasonable agreement was obtained between model and experiment for a variety of deformation conditions. Analysis of the model parameters and experimental data indicated that the nucleation density for recrystallization depended only on the applied strain for the range of deformation conditions imposed. In addition the mobility of recrystallizing boundaries was best explained by solute drag due to manganese atoms.     

Experimental assessment of structure and property predictions during hot working

Uniaxial compression experiments were conducted in the hot-working range for a commercial purity aluminum alloy using constant strain-rate tests and strain-rate drop tests producing strain hardening, strain softening, and steady-state deformation behaviors. The structure of the deformed material was characterized by microhardness and grain shape. A single internal state variable constitutive model for flow stress was developed using the microhardness data to quantify the state variable. The change in the grain aspect ratio was related to the imposed bulk strain in the samples. The constitutive model was incorporated into a finite element program. A critical experimental assessment of predictions of the spatial variation in structure and properties throughout a workpiece was then made using a tapered compression specimen. Comparisons with experimental results indicated that the load was underpredicted by 10 pct and the microhardness by 6 pct, while the severity of the strain gradients was overpredicted. This was concluded to be due to an underprediction of the work-hardening rate at low strains. Additional calculations made with alternative constitutive models showed that the internal state variable model predicted the applied force much more accurately than alternative models.     

The fracture stress of single-crystal zinc

The basal plane fracture stress of 99.999 pct pure single-crystal zinc tensile specimens was determined from 77 to 298 K as a function of strain rate. The fracture stress was found to be dependent on the size of existing flaws associated with surface preparation, when the thermal variation of surface energy was taken into account. The stress at fracture was independent of strain and strain rate and was inversely proportional to the square root of the corrected flaw size, suggesting that a Griffith-type equation was obeyed to high strains. When flaws do not exist or are negligibly small, fracture is believed to be nucleated by the splitting of subboundaries as a result of plastic flow. The strain at fracture for constant fracture stress decreases with an increase in strain rate and a decrease in temperature and depends on the values of the work-hardening coefficient and exponent.     

A new strain rate change technique for distinguishing between pure metal and alloy type creep behavior

A new technique involving strain rate changes has been developed for distinguishing between pure metal and alloy type creep behavior. Both positive and negative strain rate changes were performed on aluminum and Al-5.8 at.% Mg (pure metal and alloy type material respectively) using an Instron electromechanical testing machine. Tests were conducted at 573 K with initial total strain rates of either 4 × 10⁻⁵ or4 × 10⁻⁴s⁻¹. Immediately following an order of magnitude change in total strain rate, the plastic strain rate was monitored as a function of stress. The observed transient response for both pure aluminum and Al-5.8 Mg was found to agree with predicted behavior, indicating that the strain rate change test can be used to distinguish between pure metal and alloy type creep behavior. The strain rate change test was also found to be a promising single specimen technique for studying constant structure deformation. The quality of the constant structure data obtained using this technique is shown to depend on the accuracy with which plastic strain rate can be determined. A procedure is described for determining the plastic strain rate with sufficient accuracy to allow the strain rate change test to be used in place of multiple stress reduction tests to study constant structure deformation.     

Axisymmetric Wrinkling of Cylinders with Finite Strain

A simple analytical solution for the bifurcation buckling of a cylinder under axial loading is provided including finite-strain effects. Thus, the small strain theory result of Batterman is generalized. In addition to the thin shell theory solution (excluding shear deformations), a solution including shear deformation effects is also given. All solutions can be evaluated for either the flow or deformation theory of plasticity. The finite-strain constitutive theory used is one in which small strain type relationships apply between the Jauman rate of the Kirchhoff stress tensor and the deformation rate tensor. The analytical results are compared to finite-element analyses to test the validity of the assumptions made. The solutions are explicit. Starting with a point on the stress-strain curve, one calculates explicitly the diameter-to-thickness ratio D∕t for a cylinder that will buckle at that level of stress and strain (repeating this as necessary to generate a plot of wrinkling strains as a function of D∕t). Unless the tangent modulus at bifurcation is large compared to the stress, the results clearly indicate that finite strains have an important stabilizing effect, leading to higher bifurcation strains.     

Stress Integration Approach in Resonant Column and Torsional Shear Testing for Soils

Determination of strain in resonant column and torsional shear (RC/TS) tests is complicated due to nonuniform stress–strain variation occurring linearly with the radius in a soil specimen in torsion. The equivalent radius approach is adequate when calculating strain at low to intermediate levels, however, the approach is less accurate when performing the tests at higher strains. The stress integration approach involving integration of an assumed soil stress–strain model was developed to account for this problem more precisely. This approach was used to generate the plots of equivalent radius ratio versus strain developed based upon shear modulus and damping. Results showed that the equivalent radius ratio curves converge to a value of approximately 0.8 at low strains and decrease as strain increases. The equivalent radius ratio curves based upon damping decrease to significantly lower values at high strain than curves based upon shear modulus. This study suggests that using the same values of equivalent radius ratio to calculate strains for both shear modulus and damping is not appropriate. The stress integration approach provides an accurate analysis technique for evaluating both modulus and damping behavior of soil, over any range of strains in RC/TS testing.     

On the strain-hardening parameters of metals

The applicability of the Ludwik, Hollomon, Swift and Voce equations in describing the stress - strain curves of metals was investigated. Calculated uniform strain values were found to depend on the equation used. Even when the Hollomon equation gave a high linear correlation coefficient in log-log coordinates, the strain-hardening exponent n could give an erroneous uniform strain. The equation with the lowest standard error of estimate gave the uniform strain nearest to the value obtained by direct measurement from the load-elongation curve.     

900 MPa级析出强化钢高温变形行为

 针对900 MPa级析出强化型热轧高强钢,利用Gleeble-3800热模拟试验机研究其在变形温度为950～1 150 ℃、变形速率为0.1～10 s-1条件下的压缩变形行为。根据应力-应变曲线图获得峰值应力,并用双曲正弦方程描述热压缩变形过程中的试验钢峰值应力与Zener-Hollomon参数的关系。回归分析得到方程中变形激活能及其他材料变形参数,并对试验在高温条件下的流变应力本构方程并对其进行了验证。结果表明,采用该本构方程计算出的流变应力值与试验所得应力值非常接近,为估算成形时所需的最大载荷及设备选取提供参考。     

XRD Analysis of Local Strain Fields in Pearlitic Steels ‐ towards the Fast Examination of Microstructure after Hot Rolling

Analysis of the crystallographic anisotropy of the lattice strains, i.e. the analysis of the dependence of the lattice strain on the crystallographic direction, is discussed to be an efficient method for getting information about the mesoscopic local strains and microscopic local strain fields in dual‐phase materials. This technique is illustrated on the example of hot‐rolled pearlitic steels containing ferritic lamellae separated by cementite from each other. In these samples, the information about the local strain fields was further used to build a microstructure model that describes the interaction between crystallites of different phases on the microscopic scale. Such a microstructure model is quite appropriate for examination of the correlations between the structure and properties of the pearlitic steels, because it links the microstructure parameters obtained using X‐ray diffraction on the atomic level with the interaction between the crystallites or grains of different phases, which can more directly be related to the macroscopic mechanical properties of the materials. The second important result of this study was the detection and explanation of several correlations between individual microstructure parameters, which are obtained from X‐ray diffraction. This offers a possibility to use the X‐ray diffraction for a fast microstructure analysis of pearlitic steels, or generally for a fast microstructure analysis of dual‐phase steels, after or even during the rolling processes.     

An eulerian finite-element model for determination of deformation state of a copper subjected to orthogonal cutting

An Eulerian finite-element (FE) model was developed to predict the stress and strain distributions in the material subjected to the orthogonal machining process. Metallographic sections taken from commercially pure copper samples and subjected to orthogonal cutting were examined to determine the local strain gradients generated in the material ahead of the cutting tool tip. Local flow stress values were estimated from the microhardness measurements. Experimental flow stress and equivalent plastic strain values were found to obey a Voce-type exponential relationship, which was used in the development of the material model for the numerical simulations. The sizes of both the primary deformation zone (350 μm) and the secondary deformation zone (50 μm) predicted by the numerical model were in agreement with the experimental observations. The experimental results showed that the equivalent strain was 3.65 in the material 50 μm directly ahead of the tool tip, which compared well with the numerically observed strain (3.50). According to the numerical observations, along the primary shear plane, the high tool tip stress of 410 MPa decreased to 260 MPa near the chip root. Numerical and experimental stress and strain distributions correlated well in terms of both magnitudes and distributions, indicating that the application of an Eulerian FE approach served to predict the deformation state of the material ahead of the tool tip successfully.