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An Introduction to Materials
Published in Paul J. Hazell, Armour, 2023
where ε˙p is the effective plastic strain rate; it has the unit of s−1. The flow stress in this case is the stress taken at any point along the plastic stress–strain curve. During inelastic deformation, a considerable amount of work is converted to heat. This can lead to thermal softening of the metal where the flow strength of the material is reduced with increasing temperature. For high strain-rate applications, the process is adiabatic as there is little time for heat to be dissipated in the surrounding material. This gives rise to localized thermal softening. The effect of thermal softening on the yield strength of a metal can be described by the following equation: Y=Y0[1−(T−TrTm−Tr)m]
Influence of Nanofragmentation and Microstructural Optimization during Hot Working of Metals and Alloys
Published in T. S. Srivatsan, T. S. Sudarshan, K. Manigandan, Manufacturing Techniques for Materials, 2018
G. S. Avadhani, K. R. Y. Simha, Y. V. R. K. Prasad
The standard workability tests are discussed in detail by Dieter [2] in terms of their advantages and limitations. The classic methods involve determining flow stress by a uniform compression test or by a torsion test at temperatures and strain rates of interest. However, the widely known tensile test is not suitable since large strains cannot be achieved in this test due to the formation of a neck. On the other hand, tensile tests are useful for obtaining hot ductility. In a torsion test, large strains can be attained without the onset of geometric instability. However, disadvantages in this test are (1) strain and strain rate gradients exist from center to the surface of a solid specimen, and (2) the imposed large rotational strain results in a fiber structure. Due to its simplicity, the compression test is considered to be a standard bulk workability test in view of the following advantages:
Size Effects in Meso- and Microscaled Forming
Published in Xin Min Lai, Ming Wang Fu, Lin Fa Peng, Sheet Metal Meso- and Microforming and Their Industrial Applications, 2018
Xin Min Lai, Ming Wang Fu, Lin Fa Peng
From the perspective of design, flow stress and its hardening are very important factors, which affect material deformation, process design, and equipment selection. The flow stress in meso- and microscaled experiments was observed to be different from that of the conventional scale because of size effect, which needs to be more accurately modeled. In tandem with this, many constitutive models have been proposed to describe the size-dependent flow stress of metallic materials in microforming process. Among these models, surface layer model and grain boundary model are most representative and are summarized in the following.
An advanced dislocation density-based approach to model the tensile flow behaviour of a 64.7Ni–31.96Cu alloy
Published in Philosophical Magazine, 2022
Alen S. Joseph, Pulkit Gupta, Nilesh Kumar, Maria C. Poletti, Surya D. Yadav
The long-range contribution from dislocations, Hall–Petch contribution, short-range contribution, and total flow stress values were in the range of 455.7–485.2, 87.72, 23.60–42.65 and 567.1–615.6 MPa for deformation conducted from 0.1 to 0.0001 s−1 at 298 K and 93 µm. Higher strain rate resulted in higher rate of formation of immobile dislocation density and hence the higher flow stress response (see Figure 6(b)). High strain rate leads to higher glide velocity of dislocations resulting in enhanced operation frequency of Frank-read sources and hence producing more dislocations. Hall–Petch contributions are constant over different strain rate as Equation (15) doesn’t incorporate the strain rate influence and need to be explored as outlook. It seems that deformation at higher strain rates result in higher short-range contributions (see Figure 6(d,e)) due to the higher lattice resistance. This can be understood from Equation (17) that higher the strain rate, stress required to pass the general obstacles would be high, leading to increased short-range contribution. However, more high-temperature tests need to be carried out in order to calibrate the model, as an outlook of this work. In this work, it was also observed that the strain rates have relatively small influence on the substructural evolution as with respect to that of temperature and grain size. These results coincide with the observations found in the literature [60,61].
Microstructural evolution and flow behaviour in hot compression of as-extruded Mg–Gd–Nd–Zn–Zr alloy
Published in Philosophical Magazine, 2021
S. Mosadegh, M. Aghaie-Khafri, B. Binesh
Figure 4 shows the stress–strain curves of Mg–5Gd–2.5Nd–0.5Zn–0.5Zr alloy at 350°C, 400°C, 450°C, 500°C and strain rates of 0.001, 0.01, 0.1 and 1 s−1. It can be observed that flow stress is mainly increased by strain rate and decreased by temperature. A single peak flow curve is observed in which the flow stress generally increased due to the strain hardening until it reaches a maximum value, followed by a dynamic softening, and finally attained a steady-state stress. The steady-state condition is established by a dynamic balance between strain hardening and strain softening. The observed dynamic softening i.e. the single peak behaviour can be ascribed to the DRX. The observed flow behaviour is consistent with other investigation on Mg alloys [39–41]. It is worth mentioning that for samples deformed at 350°C and 400°C, the compressive yield point for 1 s−1 strain rate is somehow less than 0.1 s−1. The fact can be attributed to the effect of adiabatic heating which is more significant at high strain rate deformation. However, the adiabatic heating effect was not eliminated in this study mainly due to the fact that this effect is not so sophisticated at strain rates less than 1 s−1, as it is not observed for 450°C and 500°C.
Ductile fracture prediction of high tensile steel EH36 using new damage functions
Published in Ships and Offshore Structures, 2018
Sung-Ju Park, Kangsu Lee, Joonmo Choung, Carey Leroy Walters
The flow stress can be measured from a tensile test where uniform strain of gauge length can also be measured using an extensometer. After the onset of necking, the stress–strain relationship is difficult to obtain because of two reasons. The first reason is that the stress state is more complex, meaning that the stress state inside the neck can no longer be modelled with the assumption of uniaxial stress. This is typically corrected by either applying the correction of Bridgman (1952) or by inverse-engineering the stress–strain curve. In this paper, the Hollomon power law, which is fitted before the onset of necking, is extrapolated to the strains after the onset of necking (see Figure 3). The second reason causing difficulty to obtain stress–strain curve after the onset of necking is that yield loci can depend on the effect of stress triaxiality (normalised hydrostatic pressure). Bai and Wierzbicki (2010) and Mohr and Marcadet (2015) have introduced different ways of accounting for the state of stress on the yield function. For the purposes of this paper, we assume that von Mises yield locus remains valid throughout the deformation process.