Nonisothermal punch stretching: Measurements and finite element modeling simulations
- PDF / 855,720 Bytes
- 9 Pages / 597.28 x 785 pts Page_size
- 87 Downloads / 216 Views
[1]
where B is a constant less than zero and A T is the temperature difference from a standard temperature where tro is measured. An integrated constitutive law for aluminum-killed steel [241 or interstitial-free steel t471 has been proposed as follows:
tr = K ( e + eo)'(g:/gzo)m(1 + B A T )
[3]
where K, A, B, and To are constants and T is the absolute temperature. Aluminum alloys seem to fit a temperature dependence as follows: 1431 o- = tro exp [A/BT]
[4]
For small variations in temperature, the differences among the forms shown in Eqs. [1] through [4] are minor. II. E X P E R I M E N T A L A N D ANALYTICAL PROCEDURES
The present work consists of three segments: material characterization, nonisothermal hemispherical punch/ stretch experiments, and FEM simulations of the latter. The techniques used for the material characterization and the FEM simulations will be briefly outlined in the following sections. The application of these methods to the novel, heated-punch experiment is unique and forms the core of the current work.
A. Material Characterization Armco aluminum-killed, drawing-quality, uncoated steel was employed for all experiments. Its chemical composition is as follows: C-0.057 pct, S-0.009 pct, Mn-0.21 pct, N-0.14 pct, and A1-0.047 pct. The standard mechanical properties for this alloy appear in Table I. A series of standard A S T M E-8 sheet tensile tests was conducted at nominal strain rates of 1 0 - 4 / S , 1 0 - 3 / S , and 10-2/s and at ambient air temperatures of 23 ~ 25 ~ 43 ~ and 77 ~ Each experimental true stress-strain curve was fit with several standard work-hardening forms using least-squares procedures presented in detail elsewhere. 15~ T h e best fit was obtained for the Swift form (Eq. [2]), with fit coefficients presented in Table II. A detailed analysis of strain-rate sensitivity showed that m (in Eq. [2]), as determined from the continuous tensile tests only, did not vary with strain or temperature, within experimental uncertainty. For example, the variation with strain was less than 10 -5 and, at various temperatures, less than 0.003. Finally, using the knowledge that the parameters n, o'0, and m were constant in each tensile test, the effect of temperature was analyzed using the 3004--VOLUME 22A, DECEMBER 1991
Standard Mechanical Properties
Thickness Yield point elongation Yield strength Tensile strength Total elongation (50.8 mm) Rockwell hardness (B-scale) Uniform elongation Hardening coefficient, n Coefficient of anisotrop~,
[2]
where e and ~ are true strain and strain rate, respectively, and K, e0, n, e0, and m are constants expressing strain hardening and strain-rate sensitivity, while the temperature sensitivity follows Eq. [1]. Other materials have been fit to alternate forms. For example, 3 10 stainless has been modeled by 1471 6r = K[1 - A exp (Be)] (g:/g:o)"(T/To) B
Table I.
Grain structure
0.83 mm 0.0 pct 177 MPa 315 MPa 42.8 pct 39.9 24.0 pct 0.216 r0 = 1.90, r45 = 1.42, r90 = 2.28, Y = 1.75, and Ar = 0.68 ASTM 7-8, elongated
reduced variables K and T. Thi
Data Loading...
