| The mechanically-measured Young's modulus of metals is consistently lower than the physically measured one, particularly after plastic straining. Furthermore, the nominally elastic loading and unloading behavior is not linear; it shows significant curvature and hysteresis. While many reports of this so-called "modulus effect" have appeared, the consistency of the behavior among grades of steel, or within a single grade produced by alternate methods and suppliers, is unknown. That is, there is little information on whether it is necessary for manufacturers to measure and control the mechanical modulus for every coil of steel in order to guarantee accurate simulations, consistent forming, and reliable in-service behavior. In order to address these issues, 12 steels (4 diverse grades: IF, HSLA, DP600, DP980; 3 producers per grade) were subjected to high-precision modulus measurements using mechanical testing, resonant frequency damping analysis, and ultrasonic pulse-echo techniques. All of these measurements show remarkable consistency among not only suppliers but also among grades. The primary determinant of hysteresis/curvature of the stress-strain response was found to be the nominal flow stress of the alloy. Other variations of overall mechanical modulus are minor compared with hysteresis/curvature. The following conclusions were reached: 1) there is no significant difference among suppliers of a single steel grade, 2) there is very little difference between grades of steel, except for that attributable to differing strengths, 3) mechanical unloading and reloading after pre-strain are similar, 4) cyclic loading and unloading cycles have no accumulated effect except through a minor change of flow stress, and 5) the initial loading or unloading modulus is very similar to the physical modulus, but the mechanically measured slope degrades very rapidly as loading or unloading proceeds, and plateaus at even small strain (<2%).;Based on some conclusions drawn from the study on the modulus effect of twelve steels, hundreds of high-precision tensile tests of 29 commercial sheet alloys representing a wide range of material properties were performed and analyzed in further way to quantify this nonlinear behavior.;Three major conclusions were reached: (1) No significant purely elastic region can be discerned. That is, a plastic yield stress of zero fits the data as well as a finite yield stress. There is no compelling evidence of a purely elastic / linear response near zero stress or upon unloading. (2)The measured stress-strain transitional behavior is represented adequately by a simple 1-parameter equation. The parameter, A, represents the "modulus reduction rate." (3) The modulus reduction rate is found to obey a "Universal Law," depending only on the strength of the material and the physical Young's modulus, but not on the composition, the crystal structure, or other physical attributes of the alloy. These results provide an immediate pathway to greatly improving the material constitutive laws used with FE analysis for, among other things, springback analysis and structural collapse. Most importantly and surprisingly, these results suggest that no unusual or additional testing is needed to achieve significant accuracy improvements. An example case is presented. |
