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Dynamic and Time-Dependent Fracture
Published in T.L. Anderson, Fracture Mechanics, 2017
where the constants In, σ˜ij, and ε˜ij are identical to the corresponding parameters in the HRR relationship (Equation 3.25 and 3.26). Note that in the present case, n is a creep exponent rather than a strain hardening exponent.
Effect of high energy ball milling on spherical metallic powder particulates for additive manufacturing
Published in Particulate Science and Technology, 2021
Troy Y. Ansell, Timothy Hanneman, Andres Gonzalez-Perez, Chanman Park, Andy Nieto
These relationships indicate that materials with a higher strain hardening exponent will undergo greater strain hardening (e.g., strengthening) than materials with a lower strain hardening exponent for a given deformation. Cu has a strain hardening exponent ranging from n∼0.3 − 0.32 in an annealed condition (Lu et al. 2000; Fattah-alhosseini et al. 2016), to as low as ∼0.045 in a 25% pre-strained Cu specimen (Fattah-alhosseini et al. 2016). 316L stainless steel has a significantly higher strain hardening exponent of n∼0.40–0.48 at room temperature to ∼0.5 at elevated temperature (350 °C) (Samuel and Choudhary 2010; Pintaude, Hoechele, and Cipriano 2012), temperatures not atypical for HEBM processing. Hence, it is seen that the higher strain-hardening exponent of 316L steel makes it more prone to undergoing strain hardening and hence higher hardness for a given amount of deformation induced by the HEBM process. The lower strain hardening exponent of Cu allows it to be severely deformed, as evidenced by the formation of Cu flakes, with minimal increases in hardness initially. Lower, but comparable hardening to 316L SS occurs after 60 min of milling at the higher energy condition.
Quantitative analysis of microstructure refinement in ultrafine-grained strips of Al6063 fabricated using large strain extrusion machining
Published in Machining Science and Technology, 2020
Vipin Kumar Sharma, Vinod Kumar, Ravinder Singh Joshi
Where, Pmax = Maximum load applied, hmax = Maximum indentation depth, hr = Residual depth of indentation, C = Distance from center of indent to the outer periphery of elastoplastic deformation zone, E* = Reduced elastic modulus, ν and νin = Poisson’s ratio of sample and indenter, E and Ein= Effective elastic modulus of sample and indenter. σy = Yield strength of indented material, σ0.29 = Stress corresponding to the characteristic plastic strain of 0.29 for the indented material, M1 and M2 = 6.618 and −0.875, respectively for Berkovich indenter. The reduced elastic modulus (E*) was found to be 81.44 GPa for the bulk aluminium and for the fabricated strips were found to be 94.51 GPa and 87.15 GPa corresponding to the value of rake angle values 0° and 5° with cutting speed 40.47 m/min. Values of (hmax) and (hr) can be obtained from the load versus displacement curve. Table 5 portrays the values of necessary parameters for strain hardening exponent estimation and the calculated value of (n) for bulk and fabricated strips at different machining conditions. The value of (n) was observed to be least in the bulkingot sample compared to the strips depicting lower internal strain which would have been acquired by the material during processing. Value of (n) for bulk was found to be 0.45 whereas for strips was found to be 0.6. Value of (n) was less in strip fabricated at 5° as compared to that of fabricated at 0°. Increase in value signifies the increase in fabricability of these strips. Numerically the value of strain hardening exponent lies between 0 and 1. A value corresponds to 0 indicates the material in the plastic solid region while the value 1 indicates a 100% elastic solid. Strain hardening exponent correlate with the ability of dislocations to move around or over dislocations called cross slip. Even at higher strain level value of this exponent increased further. Decrease in grain size results in decrease in strain hardening whereas, in bimodal microstructure at reduced grain size known to exhibit the pronounced strain hardening. Such concurrent strengthening and toughening, as observed in strips in comparison with bulk alloy, could be attributed to the bimodal microstructure observed in the strips. Strips fabricated at lower strain level show to have grain structure consist of coarse and finer grains. Moreover, with increase in strain level in these strips number of coarse grains are expected to decrease further. At very high strain level these strips may have only very fine grains. As of these fine grains, strain hardening exponent can decrease. As per observation made from the analysis, it may be concluded that strip fabricated at medium strain level may have better fabric ability than the strip fabricated at low or very high strain levels. It is found from the analysis that in LSEM process grain refinement due to high level of strain and dynamic recrystallization of grain. It leads to improve hardness and well as ductility of the material.