The discussion centers around the differences between ultimate tensile strength (UTS) and breaking stress in materials, exploring the concepts of engineering and true stress-strain curves. Participants examine the implications of these definitions and the behavior of materials under tensile loads.
Participants express differing views on the implications of UTS and breaking stress, as well as the interpretation of stress-strain curves. There is no consensus on the relationship between stress, force, and cross-sectional area after yielding.
The discussion highlights limitations in understanding the behavior of materials under stress, particularly regarding the assumptions made in engineering versus true stress calculations and the non-linear behavior of materials beyond yield points.
There is an engineering stress strain curve and a true stress strain curve. The engineering stress strain curve assumes that the member cross section area remains constant at all levels of tensile load, but in actuality, cross section starts to significantly reduce (called necking) at high stress values beyond the yield point, in which case if you plot true stress, which accounts for the reduced cross section area , versus strain, the true stress value always increases up to rupture, whereas if you use engineering stress, you get a peak on the curve prior to significant necking, and beyond that, the stress gets lower because it is assumed that cross section remains constant . The value of the engineering stress at this peak is called the ultimate tensile strength, whereas the breaking strength is the rupture stress at point of failure .Tangeton said:By definition the UTS is the maximum stress a material can take. But how exactly can a material not break after reaching the UTS if it is so? Why is there a breaking stress and how come on the graph of stress against strain the stress seems to decreases before the braking stress?
PhanthomJay said:There is an engineering stress strain curve and a true stress strain curve. The engineering stress strain curve assumes that the member cross section area remains constant at all levels of tensile load, but in actuality, cross section starts to significantly reduce (called necking) at high stress values beyond the yield point, in which case if you plot true stress, which accounts for the reduced cross section area , versus strain, the true stress value always increases up to rupture, whereas if you use engineering stress, you get a peak on the curve prior to significant necking, and beyond that, the stress gets lower because it is assumed that cross section remains constant .
But Hooke's Law does not apply after yielding, since the stress strain curve is no longer linear beyond the yield stress ( we're talking steel or aluminum as an example), and thus, increasing strain no longer implies increasing force. Ideally, when you apply an increasing tensile load to a test specimen, the elongation and strain increase as the applied load increases until yield, but then the elongation increases without much increase in the applied load, sort of like silly putty where stretching becomes extensive with no increase in applied load required.Tangeton said:I understand the point you're trying to make about cross-sectional section remaining constant, but since Stress = F/A, if A is constant, should stress be still increasing with the force applied? I know that it is a stress vs strain graph, but strain is extension over length and the bigger the extension, the larger the force from Hooke's law, so the force must be increasing with stress it would seem to me?